Showing papers in "Classical and Quantum Gravity in 2005"
TL;DR: In this article, a deformation of the algebra of diffeomorphisms is constructed for canonically deformed spaces with constant deformation parameter?, and a covariant tensor calculus is constructed based on this deformed algebra, which can be interpreted as a?-deformed Einstein?Hilbert action.
Abstract: A deformation of the algebra of diffeomorphisms is constructed for canonically deformed spaces with constant deformation parameter ?. The algebraic relations remain the same, whereas the comultiplication rule (Leibniz rule) is different from the undeformed one. Based on this deformed algebra, a covariant tensor calculus is constructed and all the concepts such as metric, covariant derivatives, curvature and torsion can be defined on the deformed space as well. The construction of these geometric quantities is presented in detail. This leads to an action invariant under the deformed diffeomorphism algebra and can be interpreted as a ?-deformed Einstein?Hilbert action. The metric or the vierbein field will be the dynamical variable as they are in the undeformed theory. The action and all relevant quantities are expanded up to second order in ?.
556 citations
TL;DR: In this paper, the mass and angular momenta of rotating black holes in anti-de Sitter backgrounds in four, five and higher dimensions have been obtained, and it has been shown that the associated thermodynamic potential equals the background subtracted Euclidean action multiplied by the temperature.
Abstract: We obtain expressions for the mass and angular momenta of rotating black holes in anti-de Sitter backgrounds in four, five and higher dimensions. We verify explicitly that our expressions satisfy the first law of thermodynamics, thus allowing an unambiguous identification of the entropy of these black holes with of the area. We find that the associated thermodynamic potential equals the background-subtracted Euclidean action multiplied by the temperature. Our expressions differ from many given in the literature. We find that in more than four dimensions, only our expressions satisfy the first law of thermodynamics. Moreover, in all dimensions we show that our expression for the mass coincides with that given by the conformal conserved charge introduced by Ashtekar, Magnon and Das. We indicate the relevance of these results to the AdS/CFT correspondence.
536 citations
TL;DR: In this article, a non-canonical complex scalar field is proposed as the dark energy to avoid the difficulty of the Q-ball formation which gives trouble to the spintessence model.
Abstract: Recently a lot of attention has been given to building a dark energy model in which the equation-of-state parameter w can cross the phantom divide w = -1. One of the models to realize crossing the phantom divide is called the quintom model, in which two real scalar fields appear, one is a normal scalar field and the other is a phantom-type scalar field. In this paper we propose a non-canonical complex scalar field as the dark energy, which we dub 'hessence', to implement crossing the phantom divide, in a similar sense as the quintom dark energy model. In the hessence model, the dark energy is described by a single field with an internal degree of freedom rather than two independent real scalar fields. However, the hessence is different from an ordinary complex scalar field, we show that the hessence can avoid the difficulty of the Q-ball formation which gives trouble to the spintessence model (an ordinary complex scalar field acts as the dark energy). Furthermore, we find that, by choosing a proper potential, the hessence could correspond to a Chaplygin gas at late,times.
351 citations
TL;DR: A new numerical scheme to solve the Einstein field equations based upon the generalized harmonic decomposition of the Ricci tensor is introduced and a variant of the cartoon method for efficiently simulating axisymmetric spacetimes with a Cartesian code is described.
Abstract: A new numerical scheme to solve the Einstein field equations based upon the generalized harmonic decomposition of the Ricci tensor is introduced. The source functions driving the wave equations that define generalized harmonic coordinates are treated as independent functions, and encode the coordinate freedom of solutions. Techniques are discussed to impose particular gauge conditions through a specification of the source functions. A 3D, free evolution, finite difference code implementing this system of equations with a scalar field matter source is described. The second-order-in-space-and-time partial differential equations are discretized directly without the use of first-order auxiliary terms, limiting the number of independent functions to 15—ten metric quantities, four source functions and the scalar field. This also limits the number of constraint equations, which can only be enforced to within truncation error in a numerical free evolution, to four. The coordinate system is compactified to spatial infinity in order to impose physically motivated, constraint-preserving outer boundary conditions. A variant of the cartoon method for efficiently simulating axisymmetric spacetimes with a Cartesian code is described that does not use interpolation, and is easier to incorporate into existing adaptive mesh refinement packages. Preliminary test simulations of vacuum black-hole evolution and black-hole formation via scalar field collapse are described, suggesting that this method may be useful for studying many spacetimes of interest.
334 citations
TL;DR: In this paper, the authors review what is known about this reduction, mainly within the context of pure (2 + 1)-dimensional gravity, and discuss its implications for our understanding of the statistical mechanics and quantum mechanics of black holes.
Abstract: In three spacetime dimensions, general relativity becomes a topological field theory, whose dynamics can be largely described holographically by a two-dimensional conformal field theory at the 'boundary' of spacetime. I review what is known about this reduction—mainly within the context of pure (2 + 1)-dimensional gravity—and discuss its implications for our understanding of the statistical mechanics and quantum mechanics of black holes.
310 citations
TL;DR: In this paper, it is shown that in GR plus a term containing a negative power of curvature, cosmic speed-up may be achieved while the effective phantom phase (with w less than −1) follows when such a term contains a fractional positive power of curve curvature.
Abstract: We discuss modified gravity which includes negative and positive powers of curvature and provides gravitational dark energy. It is shown that in GR plus a term containing a negative power of curvature, cosmic speed-up may be achieved while the effective phantom phase (with w less than −1) follows when such a term contains a fractional positive power of curvature. Minimal coupling with matter makes the situation more interesting: even 1/R theory coupled with the usual ideal fluid may describe the (effective phantom) dark energy. The account of the R2 term (consistent modified gravity) may help to escape cosmic doomsday.
310 citations
TL;DR: In this article, a detailed analysis of dynamics of cosmological models based on Rn gravity is presented, which can be written as a first-order autonomous system and analyzed using the standard techniques of dynamical system theory.
Abstract: A detailed analysis of dynamics of cosmological models based on Rn gravity is presented. We show that the cosmological equations can be written as a first-order autonomous system and analysed using the standard techniques of dynamical system theory. In the absence of perfect fluid matter, we find exact solutions whose behaviour and stability are analysed in terms of the values of the parameter n. When matter is introduced, the nature of the (non-minimal) coupling between matter and higher order gravity induces restrictions on the allowed values of n. Selecting such intervals of values and following the same procedure used in the vacuum case, we present exact solutions and analyse their stability for a generic value of the parameter n. From this analysis emerges the result that for a large set of initial conditions an accelerated expansion is an attractor for the evolution of the Rn cosmology. When matter is considered a transient almost-Friedman phase can also be present before the transition to accelerated expansion.
303 citations
TL;DR: In this paper, a paradigm describing black hole evaporation in nonperturbative quantum gravity is developed by combining two sets of detailed results: (i) resolution of the Schwarzschild singularity using quantum geometry methods and (ii) time evolution of black holes in the trapping and dynamical horizon frameworks.
Abstract: A paradigm describing black hole evaporation in non-perturbative quantum gravity is developed by combining two sets of detailed results: (i) resolution of the Schwarzschild singularity using quantum geometry methods and (ii) time evolution of black holes in the trapping and dynamical horizon frameworks. Quantum geometry effects introduce a major modification in the traditional spacetime diagram of black hole evaporation, providing a possible mechanism for recovery of information that is classically lost in the process of black hole formation. The paradigm is developed directly in the Lorentzian regime and necessary conditions for its viability are discussed. If these conditions are met, much of the tension between expectations based on spacetime geometry and structure of quantum theory would be resolved.
296 citations
TL;DR: In this paper, the authors used a spherically symmetric Lagrangian code and studied both supercritical perturbations, which go on to produce black holes, and sub-critical perturbs, for which the overdensity eventually disperses into the background medium.
Abstract: Results are presented from general relativistic numerical computations of primordial black-hole formation during the radiation-dominated era of the universe. Growing-mode perturbations are specified within the linear regime and their subsequent evolution is followed as they become nonlinear. We use a spherically symmetric Lagrangian code and study both super-critical perturbations, which go on to produce black holes, and sub-critical perturbations, for which the overdensity eventually disperses into the background medium. For super-critical perturbations, we confirm the results of previous work concerning scaling laws but note that the threshold amplitude for a perturbation to lead to black-hole formation is substantially reduced when the initial conditions are taken to represent purely growing modes. For sub-critical cases, where an initial collapse is followed by a subsequent re-expansion, strong compressions and rarefactions are seen for perturbation amplitudes near to the threshold. We have also investigated the effect of including a significant component of vacuum energy and have calculated the resulting changes in the threshold and in the slope of the scaling law.
286 citations
TL;DR: In this paper, the authors consider a generalized class of similar models that exhibit continuous pressure without the presence of infinitesimally thin shells and find that anisotropic pressures in the "crust" of a gravastar-like object are unavoidable.
Abstract: One of the very small number of serious alternatives to the usual concept of an astrophysical black hole is the 'gravastar' model developed by Mazur and Mottola, and a related phase-transition model due to Laughlin et al. We consider a generalized class of similar models that exhibit continuous pressure—without the presence of infinitesimally thin shells. By considering the usual TOV equation for static solutions with negative central pressure, we find that gravastars cannot be perfect fluids—anisotropic pressures in the 'crust' of a gravastar-like object are unavoidable. The anisotropic TOV equation can then be used to bound the pressure anisotropy. The transverse stresses that support a gravastar permit a higher compactness than is given by the Buchdahl–Bondi bound for perfect-fluid stars. Finally, we comment on the qualitative features of the equation of state that gravastar material must have if it is to do the desired job of preventing horizon formation.
272 citations
TL;DR: In this article, the authors review aspects of loop quantum gravity in a pedagogical manner, with the aim of enabling a precise but critical assessment of its achievements so far, emphasizing that the off-shell closure of the constraint algebra is a crucial test of quantum spacetime covariance, and thereby of the consistency, of the theory.
Abstract: We review aspects of loop quantum gravity in a pedagogical manner, with the aim of enabling a precise but critical assessment of its achievements so far. We emphasize that the off-shell ('strong') closure of the constraint algebra is a crucial test of quantum spacetime covariance, and thereby of the consistency, of the theory. Special attention is paid to the appearance of a large number of ambiguities, in particular in the formulation of the Hamiltonian constraint. Developing suitable approximation methods to establish a connection with classical gravity on the one hand, and with the physics of elementary particles on the other, remains a major challenge.
TL;DR: In this article, the dynamics in three-dimensional loop quantum gravity with zero cosmological constant were studied and a rigorous definition of Rovelli's generalized projection operator from the kinematical Hilbert space to the physical Hilbert space was provided.
Abstract: In this paper, we address the problem of the dynamics in three-dimensional loop quantum gravity with zero cosmological constant. We construct a rigorous definition of Rovelli's generalized projection operator from the kinematical Hilbert space—corresponding to the quantization of the infinite-dimensional kinematical configuration space of the theory—to the physical Hilbert space. In particular, we provide the definition of the physical scalar product which can be represented in terms of a sum over (finite) spin-foam amplitudes. Therefore, we establish a clear-cut connection between the canonical quantization of three-dimensional gravity and spin-foam models. We emphasize two main properties of the result: first that no cut-off in the kinematical degrees of freedom of the theory is introduced (in contrast to standard 'lattice' methods), and second that no ill-defined sum over spins ('bubble' divergences) are present in the spin-foam representation.
TL;DR: This article derived Hamiltonian generators of asymptotic symmetries for general relativity with boundary conditions using the "covariant phase space" method of Wald et al. They then compared their results with other definitions that have been proposed in the literature, including the spinor definition, and with the background-dependent definition of Henneaux and Teitelboim.
Abstract: We derive Hamiltonian generators of asymptotic symmetries for general relativity with asymptotic AdS boundary conditions using the 'covariant phase space' method of Wald et al. We then compare our results with other definitions that have been proposed in the literature. We find that our definition agrees with that proposed by Ashtekar et al, with the spinor definition, and with the background-dependent definition of Henneaux and Teitelboim. Our definition disagrees with that obtained from the 'counterterm subtraction method', but the difference is found to consist only of a 'constant offset' that is determined entirely in terms of the boundary metric. We finally discuss and justify our boundary conditions by a linear perturbation analysis, and we comment on generalizations of our boundary conditions, as well as inclusion of matter fields.
TL;DR: The loop quantum gravity approach as mentioned in this paper is a variant of the canonical approach, the oldest being quantum geometrodynamics where the fundamental configuration variable is the three-metric Loop quantum gravity has developed from a new choice of canonical variables introduced by Abhay Ashtekar in 1986, the new configuration variable being a connection defined on a three-manifold Instead of the connection itself, the loop approach employs a non-local version in which the connection is integrated over closed loops This is similar to the Wilson loops used in gauge theories.
Abstract: The most difficult unsolved problem in fundamental theoretical physics is the consistent implementation of the gravitational interaction into a quantum framework, which would lead to a theory of quantum gravity Although a final answer is still pending, several promising attempts do exist Despite the general title, this book is about one of them - loop quantum gravity This approach proceeds from the idea that a direct quantization of Einstein's theory of general relativity is possible In contrast to string theory, it presupposes that the unification of all interactions is not needed as a prerequisite for quantum gravity Usually one divides theories of quantum general relativity into covariant and canonical approaches Covariant theories employ four-dimensional concepts in its formulation, one example being the path integral approach Canonical theories start from a classical Hamiltonian version of the theory in which spacetime is foliated into spacelike hypersurfaces Loop quantum gravity is a variant of the canonical approach, the oldest being quantum geometrodynamics where the fundamental configuration variable is the three-metric Loop quantum gravity has developed from a new choice of canonical variables introduced by Abhay Ashtekar in 1986, the new configuration variable being a connection defined on a three-manifold Instead of the connection itself, the loop approach employs a non-local version in which the connection is integrated over closed loops This is similar to the Wilson loops used in gauge theories Carlo Rovelli is one of the pioneers of loop quantum gravity which he started to develop with Lee Smolin in two papers written in 1988 and 1990 In his book, he presents a comprehensive and competent overview of this approach and provides at the same time the necessary technical background in order to make the treatment self-contained In fact, half of the book is devoted to 'preparations' giving a detailed account of Hamiltonian mechanics, quantum mechanics, general relativity and other topics According to the level of the reader, this part can be skipped or studied as interesting material on its own The penetrating theme of the whole book (its leitmotiv) is background independence In non-gravitational theories, dynamical fields are formulated on a fixed background spacetime that plays the role of an absolute structure in the theory In general relativity, on the other hand, there is no background structure - all fields are dynamical This was a confusing point already during the development of general relativity and led Albert Einstein in 1913 erroneously to give up general covariance before recognizing his error and presenting his final correct field equations that are of course covariant This story is instructive, circling around the famous 'hole problem', and is told in detail in Rovelli's book Its solution is that points on a bare manifold do not make sense in physics; everything, including the gravitational field, is dragged around by a diffeomorphism - there is just no background available, only the fields exist In loop quantum gravity, physical space (called 'quantum geometry') itself is formed by loop-like quantum states: a suitable orthonormal basis is provided by spin-network states (a spin-network is a graph with edges and nodes, where spins are assigned to the edges), and the quantum geometry is a superposition of such states Time and space in the usual sense have disappeared In the second half of his book, Rovelli discusses at length the major successes of this approach First of all, the formalism yields a unique kinematical Hilbert space for the quantum states obeying the Gauss and diffeomorphism constraints The situation with the Hamiltonian constraint is more subtle The need for a Hilbert-space structure in quantum gravity is, however, not discussed After all, the Hilbert-space structure in quantum mechanics is tied to the presence of an external time and the conservation of probability with respect to this external time But in quantum gravity there is no background structure, in particular no external time Secondly, there exist two important operators that are connected, respectively, with area and volume in the classical limit These operators have a discrete spectrum and thus provide elementary 'quanta' of area and volume This gives a vague hint of a discrete structure at the Planck scale, about which there were speculations for many decades In spite of these promising results, loop quantum gravity is still far away from a physical theory This is also reflected in this volume where the technical treatment prevails and where physical applications are relegated to about 20 pages These applications deal with quantum cosmology and black holes The part on loop quantum cosmology summarizes briefly recent results about a possible singularity avoidance and a new mechanism for inflation These results are not derived from loop quantum gravity but from imposing the discrete structure of the full theory directly on the quantum cosmological models The part on black holes discusses the derivation of the Bekenstein-Hawking entropy from counting the number of relevant spin-network states Since the theory contains a free parameter (the 'Barbero-Immirzi parameter'), the best one can do is to determine this parameter by demanding that the result be the Bekenstein-Hawking entropy The book does not yet contain the results of recent papers, published in 2004, that correct the earlier entropy calculations presented here From the new value of the Barbero-Immirzi parameter, the appealing connection with quasi-normal modes, as discussed in the book, may be lost The book concludes with a brief discussion of the major open issues Among these are the following: a well-defined and physically sensible semiclassical limit, the precise form of the Hamiltonian, the role of unification (most of the work in loop quantum gravity deals only with pure gravity) and, last but not least, the issue of quantitative and testable predictions Whether loop quantum gravity will become a physical theory is not clear Nor is this clear for string theory or any other approach However, loop quantum gravity provides a fascinating line of research and has much conceptual appeal The present volume gives both an introduction and a review of this approach, making it suitable for advanced students as well as experts It is certainly of interest for the readers of Classical and Quantum Gravity
TL;DR: In this article, the authors take a phenomenological approach to the study of the cosmological evolution of decaying vacuum cosmology (Λ(t)CDM) based on a simple assumption about the form of the modified matter expansion rate.
Abstract: We take a phenomenological approach to the study of the cosmological evolution of decaying vacuum cosmology (Λ(t)CDM) based on a simple assumption about the form of the modified matter expansion rate. In this framework, almost all current vacuum decaying models can be unified in a simple manner. We argue that the idea of letting vacuum decay to resolve the fine-tuning problem is inconsistent with cosmological observations. We also discuss some issues in confronting Λ(t)CDM with observation. Using the effective equation-of-state formalism, we indicate that Λ(t)CDM is a possible candidate for phantom cosmology. Moreover, confronted with a possible problem with the effective equation-of-state formalism, we construct the effective dark energy density. Finally, we discuss the evolution of linear perturbation.
TL;DR: The Reissner-Nordstrom black hole in four dimensions can be made unstable without violating the dominant energy condition by introducing a real massive scalar with non-renormalizable interactions with the gauge field.
Abstract: The Reissner–Nordstrom black hole in four dimensions can be made unstable without violating the dominant energy condition by introducing a real massive scalar with non-renormalizable interactions with the gauge field. New stable black hole solutions then exist with greater entropy for fixed mass and charge than the Reissner–Nordstrom solution. In these new solutions, the scalar condenses to a non-zero value near the horizon. Various generalizations of these hairy black holes are discussed, and an attempt is made to characterize when black hole hair can occur.
TL;DR: In this article, it was shown that by adding suitable lower-order terms to the Z4 formulation of the Einstein equations, all constraint violations except constant modes are damped, and that the same method can be used to damp all constraints in the Einstein equation in harmonic gauge.
Abstract: We show that by adding suitable lower-order terms to the Z4 formulation of the Einstein equations, all constraint violations except constant modes are damped. This makes the Z4 formulation a particularly simple example of a ?-system as suggested by Brodbeck et al (1999 J. Math. Phys. 40 909). We also show that the Einstein equations in harmonic coordinates can be obtained from the Z4 formulation by a change of variables that leaves the implied constraint evolution system unchanged. Therefore, the same method can be used to damp all constraints in the Einstein equations in harmonic gauge.
TL;DR: In this paper, the authors proposed a new method to solve the Killing spinor equations of 11-dimensional supergravity based on a description of spinors in terms of forms and on the spin(1, 10) gauge symmetry of the supercovariant derivative.
Abstract: We propose a new method to solve the Killing spinor equations of 11-dimensional supergravity based on a description of spinors in terms of forms and on the Spin(1, 10) gauge symmetry of the supercovariant derivative. We give the canonical form of Killing spinors for backgrounds preserving two supersymmetries, N = 2, provided that one of the spinors represents the orbit of Spin(1, 10) with stability subgroup SU(5). We directly solve the Killing spinor equations of N = 1 and some N = 2, N = 3 and N = 4 backgrounds. In the N = 2 case, we investigate backgrounds with SU(5) and SU(4) invariant Killing spinors and compute the associated spacetime forms. We find that N = 2 backgrounds with SU(5) invariant Killing spinors admit a timelike Killing vector and that the space transverse to the orbits of this vector field is a Hermitian manifold with an SU(5)-structure. Furthermore, N = 2 backgrounds with SU(4) invariant Killing spinors admit two Killing vectors, one timelike and one spacelike. The space transverse to the orbits of the former is an almost Hermitian manifold with an SU(4)-structure. The spacelike Killing vector field leaves the almost complex structure invariant. We explore the canonical form of Killing spinors for backgrounds preserving more than two supersymmetries, N > 2. We investigate a class of N = 3 and N = 4 backgrounds with SU(4) invariant spinors. We find that in both cases the space transverse to a timelike vector field is a Hermitian manifold equipped with an SU(4)-structure and admits two holomorphic Killing vector fields. We also present an application to M-theory Calabi–Yau compactifications with fluxes to one dimension.
TL;DR: In this paper, the cosmological evolution based on a D-dimensional action in low-energy effective string theory in the presence of second-order curvature corrections and a modulus scalar field (a dilaton or compactification modulus).
Abstract: We study the cosmological evolution based on a D-dimensional action in low-energy effective string theory in the presence of second-order curvature corrections and a modulus scalar field (a dilaton or compactification modulus). A barotropic perfect fluid coupled to the scalar field is also allowed. Phase space analysis and the stability of asymptotic solutions are performed for a number of models which include (i) a fixed scalar field, (ii) a linear dilaton in the string frame, and (iii) a logarithmic modulus in the Einstein frame. We confront analytical solutions with observational constraints for the deceleration parameter and show that Gauss-Bonnet gravity alone (i.e., with no matter fields) may not explain the current acceleration of the universe. We also study the future evolution of the universe using the Gauss-Bonnet parametrization and find that big rip singularities can be avoided even in the presence of a phantom fluid because of the balance between the fluid and curvature corrections. A non-minimal coupling between the fluid and the modulus field also opens up the interesting possibility of avoiding a big rip regardless of the details of the fluid equation of state.
TL;DR: In this article, the authors present an extensive catalogue of cosmological milestones, both at the kinematical and dynamical level, and derive necessary and sufficient conditions for the existence of such events.
Abstract: Until recently, the physically relevant singularities occurring in FRW cosmologies had traditionally been thought to be limited to the 'big bang', and possibly a 'big crunch'. However, over the last few years, the zoo of cosmological singularities considered in the literature has become considerably more extensive, with 'big rips' and 'sudden singularities' added to the mix, as well as renewed interest in nonsingular cosmological events such as 'bounces' and 'turnarounds'. In this paper we present an extensive catalogue of such cosmological milestones, both at the kinematical and dynamical level. First, using generalized power series, purely kinematical definitions of these cosmological events are provided in terms of the behaviour of the scale factor a(t). The notion of a 'scale-factor singularity' is defined, and its relation to curvature singularities (polynomial and differential) is explored. Second, dynamical information is extracted by using the Friedmann equations (without assuming even the existence of any equation of state) to place constraints on whether or not the classical energy conditions are satisfied at the cosmological milestones. We use these considerations to derive necessary and sufficient conditions for the existence of cosmological milestones such as bangs, bounces, crunches, rips, sudden singularities and extremality events. Since the classification is extremely general and, modulo certain technical assumptions, is complete, the corresponding results are to a high degree model independent: in particular, we provide a characterization of the class of bangs, crunches and sudden singularities for which the dominant energy condition is satisfied.
TL;DR: In this article, a simple Dirac-like form for the bilinear fermionic action for any Dp-brane in any supergravity background was derived, which generalizes the usual Dirac action valid in the absence of fluxes.
Abstract: The understanding of the fermionic sector of the world-volume D-brane dynamics on a general background with fluxes is crucial in several branches of string theory like, for example, the study of nonperturbative effects or the construction of realistic models living on D-branes. In this paper, we derive a new simple Dirac-like form for the bilinear fermionic action for any Dp-brane in any supergravity background, which generalizes the usual Dirac action valid in the absence of fluxes. A non-zero world-volume field strength deforms the usual Dirac operator in the action to a generalized non-canonical one. We show how the canonical form can be re-established by a redefinition of the world-volume geometry.
TL;DR: In this paper, the existence of finite-time singularities in isotropically expanding universes with weak, strong and dominant energy conditions has been shown and conditions for their emergence are given.
Abstract: We show the existence of an infinite family of finite-time singularities in isotropically expanding universes which obey the weak, strong and dominant energy conditions. We show what new type of energy condition is needed to exclude them ab initio. We also determine the conditions under which finite-time future singularities can arise in a wide class of anisotropic cosmological models. New types of finite-time singularity are possible which are characterized by divergences in the time rate of change of the anisotropic-pressure tensor. We investigate the conditions for the formation of finite-time singularities in a Bianchi-type VII0 universe with anisotropic pressures and construct specific examples of anisotropic sudden singularities in these universes.
TL;DR: In this paper, the authors considered a massless, minimally coupled scalar with a quartic self-interaction and used dimensional regularization to compute the fully renormalized scalar self-mass-squared at one and two-loop order for a state which is released in Bunch-Davies vacuum at t = 0.
Abstract: We work in the locally de Sitter background of an inflating universe and consider a massless, minimally coupled scalar with a quartic self-interaction. We use dimensional regularization to compute the fully renormalized scalar self-mass-squared at one- and two-loop order for a state which is released in Bunch–Davies vacuum at t = 0. Although the field strength and coupling constant renormalizations are identical to those of flat space, the geometry induces a non-zero mass renormalization. The finite part also shows a sort of growing mass that competes with the classical force in eventually turning off this system's super-acceleration.
TL;DR: In this article, the authors present a chemical bonding process to join optical components to optical mounts to obtain high stability whilst accommodating the requirement for precise alignment procedures, which was originally developed at Stanford University for the optical telescope for the Gravity Probe B mission.
Abstract: Space-based optical systems must be made from lightweight materials which can withstand significant acceleration and temperature changes Materials such as ZERODUR®, ULE® (Ultra Low Expansion material) and silica are all potentially suitable Depending on the specific requirements of the optical system and the transmissive or reflective nature of the optical layout these materials can be used by themselves or together to fabricate optical benches The geometrical layouts of these optical systems are often very complicated and the requirements for mechanical stability very stringent, thus jointing components presents a challenge In this paper we present developments of a novel chemical bonding process, originally invented at Stanford University for bonding silica components for the optical telescope for the Gravity Probe B mission Colloquially called silicate bonding, this process utilizes hydroxide catalysis to join optical components to optical mounts to obtain high stability whilst accommodating the requirement for precise alignment procedures
TL;DR: In this article, Hartle et al. introduce a pedagogical approach to teaching general relativity, which he convincingly argues should be done in the standard undergraduate physics curriculum, emphasizing physical phenomena and minimising mathematical formalism.
Abstract: The ever growing relevance of general relativity to astrophysics and cosmology continues to motivate the publication of new textbooks which put the theory in a fresh perspective informed by recent developments. In the last few years we have witnessed the appearance of two new books which reflect this trend, and which stand proud among the classic relativity texts. While the 1970s were the decade of Weinberg [1] and Misner et al [2], and the 80s the decade of Schutz [3] and Wald [4], this is clearly the decade of Hartle [5] and Carroll. Hartle has introduced a novel pedagogical approach to teaching general relativity, which he convincingly argues [6] should be done in the standard undergraduate physics curriculum. His 'physics-first approach' emphasizes physical phenomena and minimizes mathematical formalism. Hartle achieves a lot by introducing only the spacetime metric and the geodesic equation, which are the main tools needed to explore curved spacetime and extract physical consequences. To be sure, to explain how the metric is obtained in the first place does require a background of differential geometry and the formulation of the Einstein field equations. But in Hartle's book this material is wisely presented at a later stage, after an ample sampling of the physics of curved spacetime has motivated the need for the advanced mathematics. Carroll follows instead the traditional route, what Hartle calls the 'math-first approach', in which one introduces first the required mathematical formalism and only then derives the physical consequences. He is, of course, in good company, as this is the method followed in all existing textbooks (with Hartle's being the sole exception). Carroll's approach may not be original, but it is tried and true, and the result of Carroll's efforts is an excellent introduction to general relativity. The book covers the standard topics that would be found in virtually all textbooks (differential geometry, the field equations, linearized theory, black holes, and cosmology), but in addition it contains topics (such as quantum field theory in curved spacetime) which can rarely be found in introductory texts. All these topics are presented with authority and in great pedagogical style. I enjoy the book's informal, even conversational, tone, which helps Carroll establish a good rapport with the reader. All in all, this is a very usable text that offers a modern, viable alternative to existing books. My favourite part of the book is the first three chapters on differential geometry. The presentation of the mathematical formalism is crystal clear and very enjoyable, and it comes with a large number of helpful (and attractive) diagrams. Carroll's presentation of differential geometry is sophisticated but completely accessible, and it is quite broad. It includes all the topics that might be considered elementary (such as vectors and tensors, parallel transport, geodesics and curvature), but also a number of topics that might be considered advanced (such as differential forms, nonmetric connections, torsion, Lie differentiation and Killing vectors). Another particularly successful chapter is the fourth, which presents the Einstein field equations. These are first motivated in the usual way (as the simplest tensorial generalization of Poisson's equation), but are then derived from a variational principle. (This is done in the absence of the action's boundary term, whose inclusion would complicate matters and require machinery that Carroll does not introduce.) What I like most about this chapter is that alternative theories of gravitation (such as scalar-tensor theories and higher-dimensional versions of general relativity) get a fairly detailed treatment. Alternatives to general relativity are hardly ever discussed in textbooks, and this is a welcome initiative. The book's next two chapters are devoted to black holes. Carroll's treatment of the Schwarzschild spacetime is very detailed and complete, but his discussion of the Reissner-Nordstrom and Kerr spacetimes is far more sketchy. I would have liked to see an equally detailed presentation of these spacetimes. Carroll also provides a good descriptive account of the general properties of black-hole spacetimes. The book's seventh chapter contains a very enjoyable discussion of the linearized approximation to general relativity. The traditional presentation of this topic makes immediate use of the Lorenz gauge condition, which tends to create the (wrong) impression that all components of the gravitational field are radiative. With his careful treatment of gauge transformations, and his exploration of different gauge conditions, Carroll achieves the best textbook presentation of linearized theory to date. The theory is applied to calculate the deflection of light in a weak static field, and to the propagation of gravitational waves in flat spacetime. Less successfully, however, it is also applied to the generation of gravitational waves. Carroll presents the usual derivation of the quadrupole formula but fails to mention that the linearized theory is not an adequate foundation in the context of self-gravitating systems. It is a pity that the application of the quadrupole formula to binary stars does not come with such an important warning. Carroll next moves on to cosmology, a field of research that evolves so rapidly that any new textbook runs the risk of becoming rapidly outdated. This coverage of cosmology is well informed by the recent spectacular developments (including the supernovae data which reveal an accelerated expansion and the mapping of the anisotropies of the cosmic microwave background radiation (CMBR) which reveals a spatially flat universe). Carroll's presentation also includes a pedagogical account of the inflation paradigm, which has become an integral part of the standard cosmological model. This chapter, however, more than any other, left me wanting for more. I am disappointed that it contains no discussion of cosmological perturbations; this is a surprising omission, since the presentation of the linearized theory in chapter 7 is so clearly inspired by the cosmological problem. I am equally disappointed not to find a detailed discussion of the CMBR anisotropies; this omission also is surprising, since the peak structure of their multipole moments makes such a compelling case for inflationary ideas. Given that Carroll is a working cosmologist, it is indeed a surprise to me that this chapter on cosmology happens to be so brief. The ninth and final chapter of Carroll's book is devoted to a topic that has never been covered in an introductory text: quantum field theory in curved spacetime. To include this was a truly inspired thought, and Carroll is to be congratulated for this initiative. Quantum-field processes play an essential role in the physics of structure formation in the early universe, and they give rise to the famous Hawking effect which causes a black hole to behave as a thermal body. A complete education in general relativity cannot exclude this important subject, and we now have a textbook which presents it in a clear, accessible way. In summary, I am positively impressed by this book, in spite of the fact that I find it to be flawed in certain places. I firmly believe that the book stands proud among the best relativity texts. Would I use it in a general relativity course? The answer is: surely, given the right group of students. In the past I have had the pleasure of teaching both an introductory course for undergraduates and an advanced course for graduate students. In my opinion, none of these student groups are a good match for Carroll's book. For the undergraduate course I would choose Hartle over Carroll, as I much favour the physics-first approach. For the graduate course I rely on an existing working knowledge of general relativity and I cover advanced topics that are not found in Carroll's text. The right target group, I imagine, would be graduate students enrolled in an introductory course on general relativity. These students would require more sophistication than can be found in Hartle's book, and they would likely be a great match for Carroll's text. References [1] Weinberg S 1972 Gravitation and cosmology: Principles and applications of the general theory of relativity (New York: Wiley) [2] Misner C W, Thorne K S and Wheeler J A 1973 Gravitation (San Francisco: Freeman) [3] Schutz B F 1985 A First Course in General Relativity (Cambridge: Cambridge University Press) [4] Wald R M 1984 General Relativity (Chicago, IL: Chicago University Press) [5] Hartle J B 2003 Gravity: An Introduction to Einstein's General Relativity (San Francisco: Addison Wesley) [6] Hartle J B 2005 General relativity in the undergraduate physics curriculum Preprint gr-qc/0506075
TL;DR: In this article, a theory of evolving three-dimensional conformal Riemannian geometries obtained by imposing two general principles: (1) time is derived from change; (2) motion and size are relative.
Abstract: When constructing general relativity (GR), Einstein required 4D general covariance. In contrast, we derive GR (in the compact, without boundary case) as a theory of evolving three-dimensional conformal Riemannian geometries obtained by imposing two general principles: (1) time is derived from change; (2) motion and size are relative. We write down an explicit action based on them. We obtain not only GR in the CMC gauge, in its Hamiltonian 3 + 1 reformulation, but also all the equations used in York's conformal technique for solving the initial-value problem. This shows that the independent gravitational degrees of freedom obtained by York do not arise from a gauge fixing but from hitherto unrecognized fundamental symmetry principles. They can therefore be identified as the long-sought Hamiltonian physical gravitational degrees of freedom.
TL;DR: In this article, the de Sitter attractor and the big rip were determined and classified in terms of attractors and unstable points by using phase trajectories analysis for the dark energy case.
Abstract: Dark energy with the usually used equation of state p = wp, where w = const 0) and unstable (a < 0) fluids. In particular, the considered cosmological model describes the hydrodynamically stable dark (and phantom) energy. The possible types of cosmological scenarios in this model are determined and classified in terms of attractors and unstable points by using phase trajectories analysis. For the dark energy case, some distinctive types of cosmological scenarios are possible: (i) the universe with the de Sitter attractor at late times, (ii) the bouncing universe, (iii) the universe with the big rip and with the anti-big rip. In the framework of a linear equation of state the universe filled with a phantom energy, w < -1; may have either the de Sitter attractor or the big rip.
TL;DR: In this article, the authors compute correlation functions in the AdS3/CFT2 correspondence to study the emergence of effective spacetime geometries describing complex underlying microstates, and show that almost all micro states of fixed charges lie close to certain 'typical' configurations.
Abstract: We compute correlation functions in the AdS3/CFT2 correspondence to study the emergence of effective spacetime geometries describing complex underlying microstates. The basic argument is that almost all microstates of fixed charges lie close to certain 'typical' configurations. These give a universal response to generic probes, which is captured by an emergent geometry. The details of the microstates can only be observed by atypical probes. We compute two-point functions in typical ground states of the Ramond sector of the D1–D5 CFT, and compare with bulk two-point functions computed in asymptotically AdS3 geometries. For large central charge (which leads to a good semiclassical limit), and sufficiently small time separation, a typical Ramond ground state of vanishing R-charge has the M = 0 BTZ black hole as its effective description. At large time separation this effective description breaks down. The CFT correlators we compute take over, and give a response whose details depend on the microstate. We also discuss typical states with nonzero R-charge, and argue that the effective geometry should be a singular black ring. Our results support the argument that a black hole geometry should be understood as an effective coarse-grained description that accurately describes the results of certain typical measurements, but breaks down in general.
TL;DR: In this paper, the relevant expressions related to the Regge-Wheeler and Zerilli equations for the odd and even-parity perturbations of a Schwarzschild spacetime are reviewed.
Abstract: The theory of gauge-invariant non-spherical metric perturbations of Schwarzschild black-hole spacetimes is now well established. Yet, as different notations and conventions have been used throughout the years, the literature on the subject is often confusing and sometimes confused. The purpose of this review is to review and collect the relevant expressions related to the Regge–Wheeler and Zerilli equations for the odd and even-parity perturbations of a Schwarzschild spacetime. Special attention is paid to the form they assume in the presence of matter-sources and, for the two most popular conventions in the literature, to the asymptotic expressions and gravitational-wave amplitudes. Besides pointing out some inconsistencies in the literature, the expressions collected here could serve as a quick reference for the calculation of the perturbations of a Schwarzschild black-hole spacetime driven by generic sources and for those approaches in which gravitational waves are extracted from numerically generated spacetimes.
TL;DR: In this article, the geodesic structure of an AdS black hole was analyzed by means of a detailed analysis of the corresponding effective potentials for particles and photons, and all possible motions which are allowed by the energy levels were found.
Abstract: In this work, we find the geodesic structure of an AdS black hole. By means of a detailed analysis of the corresponding effective potentials for particles and photons, we find all possible motions which are allowed by the energy levels. Radial and non-radial trajectories were exactly evaluated for both geodesics. The orbits found were plotted in order to have a direct visualization of the allowed motions. We show that the geodesic structure of this black hole presents new types of motion not allowed by the Schwarzschild spacetime.