Showing papers in "Classical and Quantum Gravity in 2003"
TL;DR: In this article, all purely bosonic supersymmetric solutions of minimal supergravity in five dimensions are classified, and explicit examples of new solutions are given, including a large family of plane-fronted waves and a maximally superymmetric analogue of the Godel universe which lifts to a solution of 11-dimensional supergravity that preserves 20 supersymmetries.
Abstract: All purely bosonic supersymmetric solutions of minimal supergravity in five dimensions are classified. The solutions preserve either one half or all of the supersymmetry. Explicit examples of new solutions are given, including a large family of plane-fronted waves and a maximally supersymmetric analogue of the Godel universe which lifts to a solution of 11-dimensional supergravity that preserves 20 supersymmetries.
936 citations
TL;DR: In this article, the authors focus on the possibilities of detecting the various subtypes of (excited) BSs: possible signals include gravitational redshift and (micro-)lensing, emission of gravitational waves, or, in the case of a giant BS, its dark matter contribution to the rotation curves of galactic halos.
Abstract: There is accumulating evidence that (fundamental) scalar fields may exist in nature. The gravitational collapse of such a boson cloud would lead to a boson star (BS) as a new type of a compact object. As with white dwarfs and neutron stars, a limiting mass exists similarly, below which a BS is stable against complete gravitational collapse to a black hole. According to the form of the self-interaction of the basic constituents and spacetime symmetry, we can distinguish mini-, axidilaton, soliton, charged, oscillating and rotating BSs. Their compactness prevents a Newtonian approximation; however, modifications of general relativity, as in the case of Jordan?Brans?Dicke theory as a low-energy limit of strings, would provide them with gravitational memory. In general, a BS is a compact, completely regular configuration with structured layers due to the anisotropy of scalar matter, an exponentially decreasing 'halo', a critical mass inversely proportional to the constituent mass, an effective radius and a large particle number. Due to the Heisenberg principle, a completely stable branch exists, and as a coherent state, it allows for rotating solutions with quantized angular momentum. In this review, we concentrate on the fascinating possibilities of detecting the various subtypes of (excited) BSs: possible signals include gravitational redshift and (micro-)lensing, emission of gravitational waves, or, in the case of a giant BS, its dark matter contribution to the rotation curves of galactic halos.
628 citations
TL;DR: In this paper, a condition of additivity and linearity in the energymomentum tensor is introduced which allows one to obtain correct limits to known solutions for the electromagnetic static field, implying the relativistic relation between the energy density and pressure, as well as for the extraordinary case of the cosmological constant.
Abstract: We present new static spherically symmetric exact solutions of the Einstein equations for quintessential matter surrounding a black hole, charged or uncharged, as well as for the case without a black hole. A condition of additivity and linearity in the energy–momentum tensor is introduced which allows one to obtain correct limits to known solutions for the electromagnetic static field, implying the relativistic relation between the energy density and pressure, as well as for the extraordinary case of the cosmological constant, i.e. de Sitter space. We classify the horizons, which evidently reveal themselves in static coordinates, and derive the Gibbons–Hawking temperatures. An example of quintessence with state parameter w = −2/3 is discussed in detail.
593 citations
TL;DR: In this paper, the authors present a review of spin foam formulations of nonperturbative (background-independent) quantum gravity and define the Barrett-Crane model for four-dimensional gravity.
Abstract: In this topical review, we review the present status of the spin foam formulation of non-perturbative (background-independent) quantum gravity. The topical review is divided into two parts. In the first part, we present a general introduction to the main ideas emphasizing their motivation from various perspectives. Riemannian three-dimensional gravity is used as a simple example to illustrate conceptual issues and the main goals of the approach. The main features of the various existing models for four-dimensional gravity are also presented here. We conclude with a discussion of important questions to be addressed in four dimensions (gauge invariance, discretization independence, etc). In the second part, we concentrate on the definition of the Barrett–Crane model. We present the main results obtained in this framework from a critical perspective. Finally, we review the combinatorial formulation of spin foam models based on the dual group field theory technology. We present the Barrett–Crane model in this framework and review the finiteness results obtained for both its Riemannian and its Lorentzian variants.
571 citations
TL;DR: In this article, the authors reviewed the consequences of the brane world cosmology in a pedagogical manner and investigated the cosmology of a system with two branes and a bulk scalar field.
Abstract: Cosmological consequences of the brane world scenario are reviewed in a pedagogical manner. According to the brane world idea, the standard model particles are confined on a hypersurface (a so-called brane), which is embedded in a higher-dimensional spacetime (the so-called bulk). We begin our review with the simplest consistent brane world model: a single brane embedded in a five-dimensional anti-de Sitter spacetime. Then we include a scalar field in the bulk and discuss in detail the difference with the anti-de Sitter case. The geometry of the bulk spacetime is also analysed in some depth. Finally, we investigate the cosmology of a system with two branes and a bulk scalar field. We comment on brane collisions and summarize some open problems of brane world cosmology.
319 citations
TL;DR: In this article, the authors illustrate the conceptual problems and their solutions through a toy model: quantum mechanics of a point particle, which can also serve as a simple introduction to many of the ideas and constructions underlying quantum geometry.
Abstract: A programme was recently initiated to bridge the gap between the Planck scale physics described by loop quantum gravity and the familiar low energy world. We illustrate the conceptual problems and their solutions through a toy model: quantum mechanics of a point particle. The model can also serve as a simple introduction to many of the ideas and constructions underlying quantum geometry. Maxwell fields will be discussed in the second paper of this series which further develops the programme.
286 citations
TL;DR: In this paper, the static axisymmetric vacuum Einstein equations in more than four dimensions were solved with a ratio of maximum to minimum horizon radius of up to nine for a fixed compactification radius.
Abstract: We describe new numerical methods to solve the static axisymmetric vacuum Einstein equations in more than four dimensions. As an illustration, we study the compactified non-uniform black string phase connected to the uniform strings at the Gregory–Laflamme critical point. We compute solutions with a ratio of maximum to minimum horizon radius of up to nine. For a fixed compactification radius, the mass of these solutions is larger than the mass of the classically unstable uniform strings. Thus they cannot be the end state of the instability.
285 citations
TL;DR: In this article, a recent construction of the free-field equations for totally symmetric tensors and tensor-spinors that exhibits the corresponding linearized geometry is presented, and the higher-spin geometry is realized in free string field theory, and how the gauge fixing to the light cone can be effected.
Abstract: We review a recent construction of the free-field equations for totally symmetric tensors and tensor-spinors that exhibits the corresponding linearized geometry. These equations are not local for all spins >2, involve unconstrained fields and gauge parameters, rest on the curvatures introduced long ago by de Wit and Freedman and reduce to the local (Fang–)Fronsdal form upon partial gauge fixing. We also describe how the higher-spin geometry is realized in free string field theory, and how the gauge fixing to the light cone can be effected.
274 citations
TL;DR: The LISA project as mentioned in this paper, a joint project of ESA and NASA, is a mission that will detect and measure low-frequency signals by laser interferometry in a heliocentric orbit.
Abstract: The existence of gravitational waves is the most prominent of Einstein's predictions that has not yet been directly verified. The space project LISA shares its goal and principle of operation with the ground-based interferometers currently under construction: the detection and measurement of gravitational waves by laser interferometry. Only in space, detection of signals below, say, 1 Hz is possible. LISA, a joint project of ESA and NASA, is a mission that will measure these low-frequency waves. LISA consists of three spacecraft in heliocentric orbits, forming a triangle with 5 million km sides. Launch for LISA is scheduled for 2011, following a technology demonstrator LTP in 2006.
265 citations
TL;DR: The Gravitational N-body problem is to describe the evolution of an isolated system of N point masses interacting only through Newtonian gravitational forces as mentioned in this paper, and it is a classic problem in physics.
Abstract: The gravitational N-body problem is to describe the evolution of an isolated system of N point masses interacting only through Newtonian gravitational forces. For N =2 the solution is due to Newton. For N =3 there is no general analytic solution, but the problem has occupied generations of illustrious physicists and mathematicians including Laplace, Lagrange, Gauss and Poincare, and inspired the modern subjects of nonlinear dynamics and chaos theory. The general gravitational N-body problem remains one of the oldest unsolved problems in physics. Many-body problems can be simpler than few-body problems, and many physicists have attempted to apply the methods of classical equilibrium statistical mechanics to the gravitational N-body problem for N 1. These applications have had only limited success, partly because the gravitational force is too strong at both small scales (the interparticle potential energy diverges) and large scales (energy is not extensive). Nevertheless, we now understand a rich variety of behaviour in large-N gravitating systems. These include the negative heat capacity of isolated, gravitationally bound systems, which is the basic reason why nuclear burning in the Sun is stable; Antonov's discovery that an isothermal, self-gravitating gas in a container is located at a saddle point, rather than a maximum, of the entropy when the gas is sufficiently dense and hence is unstable (the 'gravothermal catastrophe'); the process of core collapse, in which relaxation induces a self-similar evolution of the central core of the system towards (formally) infinite density in a finite time; and the remarkable phenomenon of gravothermal oscillations, in which the central density undergoes periodic oscillations by factors of a thousand or more on the relaxation timescale - but only if N 104. The Gravitational Million-Body Problem is a monograph that describes our current understanding of the gravitational N-body problem. The authors have chosen to focus on N = 106 for two main reasons: first, direct numerical integrations of N-body systems are beginning to approach this threshold, and second, globular star clusters provide remarkably accurate physical instantiations of the idealized N-body problem with N = 105 – 106. The authors are distinguished contributors to the study of star-cluster dynamics and the gravitational N-body problem. The book contains lucid and concise descriptions of most of the important tools in the subject, with only a modest bias towards the authors' own interests. These tools include the two-body relaxation approximation, the Vlasov and Fokker-Planck equations, regularization of close encounters, conducting fluid models, Hill's approximation, Heggie's law for binary star evolution, symplectic integration algorithms, Liapunov exponents, and so on. The book also provides an up-to-date description of the principal processes that drive the evolution of idealized N-body systems - two-body relaxation, mass segregation, escape, core collapse and core bounce, binary star hardening, gravothermal oscillations - as well as additional processes such as stellar collisions and tidal shocks that affect real star clusters but not idealized N-body systems. In a relatively short (300 pages plus appendices) book such as this, many topics have to be omitted. The reader who is hoping to learn about the phenomenology of star clusters will be disappointed, as the description of their properties is limited to only a page of text; there is also almost no discussion of other, equally interesting N-body systems such as galaxies(N ≈ 106 – 1012), open clusters (N 102 – 104), planetary systems, or the star clusters surrounding black holes that are found in the centres of most galaxies. All of these omissions are defensible decisions. Less defensible is the uneven set of references in the text; for example, nowhere is the reader informed that the classic predecessor to this work was Spitzer's 1987 monograph, Dynamical Evolution of Globular Clusters, or that the standard reference on the observational properties of stellar systems is Binney and Merrifield's Galactic Astronomy. A minor irritation is that many concepts are discussed several times before they are defined, and the index provides no pointer to the primary discussion; thus, for example, there are ten index entries for 'phase mixing' and no indication that the fourth of these refers to the actual definition. The book is intended as a graduate textbook but more likely it will be used mainly in other contexts: by theoretical researchers, as an indispensable reference on the dynamics of gravitational N-body systems; by observational astronomers, as a readable summary of the theory of star cluster evolution; and by physicists seeking a well-written and accessible introduction to a simple problem that remains fascinating and incompletely understood after three centuries. Scott Tremaine
264 citations
TL;DR: In this article, the first three terms of a series expansion in the deformation parameter for a possible associative product were obtained explicitly for N = 2 Euclidean superspace, where the different conjugation relations among spinorial coordinates allow for more general supergeometry.
Abstract: We investigate the most general non(anti)commutative geometry in N = 1 four-dimensional superspace, invariant under the classical (i.e., undeformed) supertranslation group. We find that a nontrivial non(anti)commutative superspace geometry compatible with supertranslations exists with non(anti)commutation parameters which may depend on the spinorial coordinates. The algebra is in general nonassociative. Imposing associativity introduces additional constraints which, however, allow for nontrivial commutation relations involving fermionic coordinates. We obtain explicitly the first three terms of a series expansion in the deformation parameter for a possible associative -product. We also consider the case of N = 2 Euclidean superspace where the different conjugation relations among spinorial coordinates allow for a more general supergeometry.
TL;DR: In this article, an analytical continuation of the Vuorio solution to three-dimensional topologically massive gravity leads to a two-parameter family of black-hole solutions, which are geodesically complete and causally regular within a certain parameter range.
Abstract: We show that an analytical continuation of the Vuorio solution to three-dimensional topologically massive gravity leads to a two-parameter family of black-hole solutions, which are geodesically complete and causally regular within a certain parameter range. No observers can remain static in these spacetimes. We discuss their global structure, and evaluate their mass, angular momentum and entropy, which satisfy a slightly modified form of the first law of thermodynamics.
TL;DR: In this paper, the authors consider uncertainty principles which take into account the role of gravity and the possible existence of extra spatial dimensions and give explicit expressions for such generalized uncertainty principles in 4 + n dimensions and their holographic properties investigated.
Abstract: We consider uncertainty principles which take into account the role of gravity and the possible existence of extra spatial dimensions. Explicit expressions for such generalized uncertainty principles in 4 + n dimensions are given and their holographic properties investigated. In particular, we show that the predicted number of degrees of freedom enclosed in a given spatial volume matches the holographic counting only for one of the available generalizations and without extra dimensions.
TL;DR: In this article, the authors discuss obstacles to obtaining inflationary or accelerating universes in M/string theory and give an account of an old "no-go theorem" to this effect, and describe some recent ideas about the possible role of the tachyon in cosmology.
Abstract: After a pedagogical review of elementary cosmology, I go on to discuss some obstacles to obtaining inflationary or accelerating universes in M/string theory. In particular, I give an account of an old 'no-go theorem' to this effect. I then describe some recent ideas about the possible role of the tachyon in cosmology. I stress that there are many objections to a naive inflationary model based on the tachyon, but there remains the possibility that the tachyon was important in a possible pre-inflationary 'open string era' preceding our present 'closed string era'.
TL;DR: The generalized uncertainty principle, motivated by string theory and noncommutative quantum mechanics, suggests significant modifications to the Hawking temperature and evaporation process of black holes as discussed by the authors, which leads to important changes in the formation and detection of black hole at the large hadron collider.
Abstract: The generalized uncertainty principle, motivated by string theory and non-commutative quantum mechanics, suggests significant modifications to the Hawking temperature and evaporation process of black holes. For extra-dimensional gravity with Planck scale O(TeV), this leads to important changes in the formation and detection of black holes at the large hadron collider. The number of particles produced in Hawking evaporation decreases substantially. The evaporation ends when the black-hole mass is Planck scale, leaving a remnant and a consequent missing energy of order TeV. Furthermore, the minimum energy for black-hole formation in collisions is increased, and could even be increased to such an extent that no black holes are formed at LHC energies.
TL;DR: In this paper, a diagonalization of the volume operator of the Bianchi I model is shown to lead to a simplification of its volume operator such that its spectrum can be determined explicitly.
Abstract: Loop quantum cosmological methods are extended to homogeneous models in a diagonalized form. It is shown that the diagonalization leads to a simplification of the volume operator such that its spectrum can be determined explicitly. This allows the calculation of composite operators, most importantly the Hamiltonian constraint. As an application the dynamics of the Bianchi I model is studied and it is shown that its loop quantization is free of singularities.
TL;DR: In this article, loop corrections to the universal dilaton supermultiplet for type IIA strings compactified on Calabi-Yau threefolds were studied and it was shown that the corresponding quaternionic kinetic terms receive non-trivial one-loop contributions proportional to the Euler number of the Calabi Yau manifold.
Abstract: We study loop corrections to the universal dilaton supermultiplet for type IIA strings compactified on Calabi-Yau threefolds. We show that the corresponding quaternionic kinetic terms receive non-trivial one-loop contributions proportional to the Euler number of the Calabi-Yau manifold, while the higher-loop corrections can be absorbed by field ��
TL;DR: In this paper, the authors provide an overview of stellar instabilities as sources of gravitational waves, and summarize the current thinking about the detectability of gravitational wave from various scenarios, including dynamical bar-mode instability and the secular rmode instability, and provide new insights into many of the difficult issues involved in modelling unstable stars as gravitational wave sources.
Abstract: This paper provides an overview of stellar instabilities as sources of gravitational waves. The aim is to put recent work on secular and dynamical instabilities in compact stars in context, and to summarize the current thinking about the detectability of gravitational waves from various scenarios. As a new generation of kilometre length interferometric detectors is now coming online this is a highly topical theme. The review is motivated by two key questions for future gravitational-wave astronomy: are the gravitational waves from various instabilities detectable? If so, what can these gravitational-wave signals teach us about neutron star physics? Even though we may not have clear answers to these questions, recent studies of the dynamical bar-mode instability and the secular r-mode instability have provided new insights into many of the difficult issues involved in modelling unstable stars as gravitational-wave sources.
TL;DR: In this paper, closed n - 2 forms in the full interacting theory are constructed in terms of a one-parameter family of solutions to the full equations of motion that admits a reducibility parameter.
Abstract: Boundary charges in gauge theories (such as the ADM mass in general relativity) can be understood as integrals of linear conserved n - 2 forms of the free theory obtained by linearization around the background. These forms are associated one-to-one with reducibility parameters of this background (such as the time-like Killing vector of Minkowski spacetime). In this paper, closed n - 2 forms in the full interacting theory are constructed in terms of a one-parameter family of solutions to the full equations of motion that admits a reducibility parameter. These forms thus allow one to apply Stokes theorem without bulk contributions and, provided appropriate fall-off conditions are satisfied, they reduce asymptotically near the boundary to the conserved n - 2 forms of the linearized theory. As an application, the first law of black-hole mechanics in asymptotically anti-de Sitter spacetimes is derived.
TL;DR: In this paper, a geometrical model of doubly special relativity (DSR) is presented, which includes the non-commutative structure of spacetime and the phase-space algebra.
Abstract: In this paper we recall the construction of doubly special relativity (DSR) as a theory with energy–momentum space being the four-dimensional de Sitter space. Then the bases of the DSR theory can be understood as different coordinate systems on this space. We investigate the emerging geometrical picture of doubly special relativity by presenting the basis independent features of DSR that include the non-commutative structure of spacetime and the phase-space algebra. Next we investigate the relation between our geometric formulation and the one based on quantum κ-deformations of the Poincare algebra. Finally we re-derive the five-dimensional differential calculus using the geometric method, and use it to write the deformed Klein–Gordon equation and to analyse its plane-wave solutions.
TL;DR: In this article, a special plane-wave metric ds2 = 2du dv − λ(u)x2 du2 + dx2 with λ = k/u2 and k = const > 0.
Abstract: We investigate a string model defined by a special plane-wave metric ds2 = 2du dv − λ(u)x2 du2 + dx2 with λ = k/u2 and k = const > 0. This metric is a Penrose limit of some cosmological, Dp-brane and fundamental string backgrounds. Remarkably, in Rosen coordinates the metric has a 'null cosmology' interpretation with flat spatial sections and scale factor which is a power of the light-cone time u. We show that: (i) this spacetime is a Lorentzian homogeneous space. In particular, it admits a boost isometry u' = lu, v' = l−1v similar to Minkowski space. (ii) It is an exact solution of string theory when supplemented by a u-dependent dilaton such that the corresponding effective string coupling e(u) goes to zero at u = ∞ and at the singularity u = 0, reducing back-reaction effects. (iii) The classical string equations in this background become linear in the light-cone gauge and can be solved explicitly in terms of Bessel's functions, and thus the string model can be directly quantized. This allows one to address the issue of singularity at the string-theory level. We examine the propagation of first-quantized point-particle and string modes in this time-dependent background. Using an analytic continuation prescription we argue that the string propagation through the singularity can be smooth.
TL;DR: In this paper, the authors review the construction of chiral four-dimensional compactifications of type IIA string theory with intersecting D6-branes and discuss the application of these techniques to the building of models with spectrum as close as possible to the standard model, and review their main phenomenological properties.
Abstract: We review the construction of chiral four-dimensional compactifications of type IIA string theory with intersecting D6-branes. Such models lead to four-dimensional theories with non-Abelian gauge interactions and charged chiral fermions. We discuss the application of these techniques to the building of models with spectrum as close as possible to the standard model, and review their main phenomenological properties. We also emphasize the advantages/disadvantages of carrying out this idea using supersymmetric or non-supersymmetric models.
TL;DR: In this article, the authors define a level for a large class of Lorentzian Kac-Moody algebras and find the representation content of very extended AD−3 and E8 (i.e., E11) at low levels in terms of AD−1 and A10 representations.
Abstract: We define a level for a large class of Lorentzian Kac–Moody algebras. Using this we find the representation content of very extended AD−3 and E8 (i.e., E11) at low levels in terms of AD−1 and A10 representations, respectively. The results are consistent with the conjectured very extended A8 and E11 symmetries of gravity and maximal supergravity theories given respectively in preprints hep-th/0104081 and hep-th/0107209. We explain how these results provided further evidence for these conjectures.
TL;DR: In this article, it was shown that the universe is always neutrally stable with respect to small inhomogeneous vector and tensor perturbations and is stable against adiabatic scalar density inhomogeneities so long as c2s > 1/5.
Abstract: We show using covariant techniques that the Einstein static universe containing a perfect fluid is always neutrally stable against small inhomogeneous vector and tensor perturbations and neutrally stable against adiabatic scalar density inhomogeneities so long as c2s > 1/5, and unstable otherwise. We also show that the stability is not significantly changed by the presence of a self-interacting scalar field source, but we find that spatially homogeneous Bianchi type IX modes destabilize an Einstein static universe. The implications of these results for the initial state of the universe and its pre-inflationary evolution are also discussed.
TL;DR: In this article, the authors show explicitly how the Newton?Hooke groups N?10 act as symmetries of the equations of motion of non-relativistic cosmological models with a Cosmological constant.
Abstract: We show explicitly how the Newton?Hooke groups N?10 act as symmetries of the equations of motion of non-relativistic cosmological models with a cosmological constant. We give the action on the associated non-relativistic spacetimes M?4 and show how these may be obtained from a null reduction of five-dimensional homogeneous pp-wave Lorentzian spacetimes M?5. This allows us to realize the Newton?Hooke groups and their Bargmann-type central extensions as subgroups of the isometry groups of M?5. The extended Schr?dinger-type conformal group is identified and its action on the equations of motion given. The non-relativistic conformal symmetries also have applications to time-dependent harmonic oscillators. Finally we comment on a possible application to Gao's generalization of the matrix model.
TL;DR: In this paper, a discrete time description of usual quantum mechanics was obtained without any approximation or explicit discretization, which mimics features of the discrete time evolution of loop quantum cosmology.
Abstract: Inspired by the discrete evolution implied by the recent work on loop quantum cosmology, we obtain a discrete time description of usual quantum mechanics viewing it as a constrained system. This description, obtained without any approximation or explicit discretization, mimics features of the discrete time evolution of loop quantum cosmology. We discuss the continuum limit, physical inner product and matrix elements of physical observables to bring out various issues regarding the viability of a discrete evolution. We also point out how a continuous time could emerge without appealing to any continuum limit.
TL;DR: In this article, the authors investigated sources of mechanical loss in the Ta2O5/SiO2 coatings, including loss associated with the coating-substrate interface, with coating-layer interfaces and with coating materials.
Abstract: Current interferometric gravitational wave detectors use test masses with mirror coatings formed from multiple layers of dielectric materials, most commonly alternating layers of SiO2 (silica) and Ta2O5 (tantala). However, mechanical loss in the Ta2O5/SiO2 coatings may limit the design sensitivity for advanced detectors. We have investigated sources of mechanical loss in the Ta2O5/SiO2 coatings, including loss associated with the coating–substrate interface, with the coating–layer interfaces and with the coating materials. Our results indicate that the loss is associated with the coating materials and that the loss of Ta2O5 is substantially larger than that of SiO2.
TL;DR: In this article, the authors propose a new form of the C-metric with explicitly factorizable structure function G(ξ) = (1 − ξ2)(1 + 2mAξ).
Abstract: The usual form of the C-metric has the structure function G(ξ) = 1 − ξ2 − 2mAξ3, whose cubic nature can make calculations cumbersome, especially when explicit expressions for its roots are required. In this paper, we propose a new form of the C-metric, with the explicitly factorizable structure function G(ξ) = (1 − ξ2)(1 + 2mAξ). Although this form is related to the usual one by a coordinate transformation, it has the advantage that its roots are now trivial to write down. We show that this leads to potential simplifications, for example, when casting the C-metric in Weyl coordinates. These results also extend to the charged C-metric, whose structure function can be written in a new form G(ξ) = (1 − ξ2)(1 + r+Aξ)(1 + r−Aξ), where r± are the usual locations of the horizons in the Reissner–Nordstrom solution. As a by-product, we explicitly cast the extremally charged C-metric in Weyl coordinates.
TL;DR: In this article, the Campbell-Magaard theorem was extended to n dimensions and its application to current theories that postulate that our universe is a four-dimensional hypersurface within a five-dimensional manifold, such as space-time-matter (STM) theory and the Randall and Sundrum (RS) braneworld scenario.
Abstract: Stated succinctly, the original version of the Campbell–Magaard theorem says that it is always possible to locally embed any solution of four-dimensional general relativity in a five-dimensional Ricci-flat manifold. We discuss the proof of this theorem (and its variants) in n dimensions, and its application to current theories that postulate that our universe is a four-dimensional hypersurface Σ0 within a five-dimensional manifold, such as space–time–matter (STM) theory and the Randall and Sundrum (RS) braneworld scenario. In particular, we determine whether or not arbitrary spacetimes may be embedded in such theories, and demonstrate how these seemingly disparate models are interconnected. Special attention is given to the motion of test observers in five dimensions, and the circumstances under which they are confined to Σ0. For each five-dimensional scenario considered, the requirement that observers be confined to the embedded spacetime places restrictions on the 4-geometry. For example, we find that observers in the thin braneworld scenario can be localized around the brane if its total stress–energy tensor obeys the five-dimensional strong energy condition. As a concrete example of some of our technical results, we discuss a 2 symmetric embedding of the standard radiation-dominated cosmology in a five-dimensional vacuum.
TL;DR: In this paper, the first-order and second-order modified Friedmann equations are presented and the upper redshift bounds for the SNe Ia data are derived. But they are not valid for the cosmological predictions involving only the Hubble parameter.
Abstract: Recently, corrections to the Einstein-Hilbert action that become important at small curvature have been proposed. We discuss the first-order and second-order approximations to the field equations derived by the Palatini variational principle. We work out the first- and second-order modified Friedmann equations and present the upper redshift bounds when these approximations are valid. We show that the second-order effects can be neglected in the cosmological predictions involving only the Hubble parameter, e.g. the various cosmological distances, but the second-order effects cannot be neglected in the predictions involving the derivatives of the Hubble parameter. Furthermore, the modified Friedmann equations fit the SNe Ia data at an acceptable level.