Showing papers in "Classical and Quantum Gravity in 1997"
TL;DR: In this article, a functional calculus for quantum geometry is developed for a fully nonperturbative treatment of quantum gravity, which is used to begin a systematic construction of a quantum theory of geometry, and Regulated operators corresponding to 2-surfaces are introduced and shown to be self-adjoint on the underlying (kinematical) Hilbert space of states.
Abstract: A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corresponding to areas of 2-surfaces are introduced and shown to be self-adjoint on the underlying (kinematical) Hilbert space of states. It is shown that their spectra are purely discrete, indicating that the underlying quantum geometry is far from what the continuum picture might suggest. Indeed, the fundamental excitations of quantum geometry are one dimensional, rather like polymers, and the three-dimensional continuum geometry emerges only on coarse graining. The full Hilbert space admits an orthonormal decomposition into finite-dimensional subspaces which can be interpreted as the spaces of states of spin systems. Using this property, the complete spectrum of the area operators is evaluated. The general framework constructed here will be used in a subsequent paper to discuss three-dimensional geometric operators, e.g. the ones corresponding to volumes of regions.
787 citations
TL;DR: In this article, the anomalous couplings of D-brane gauge and gravitational fields to Ramond - Ramond tensor potentials were deduced by a simple anomaly inflow argument applied to intersecting Dbranes and use this to determine the 8-form gravitational coupling.
Abstract: We show that the anomalous couplings of D-brane gauge and gravitational fields to Ramond - Ramond tensor potentials can be deduced by a simple anomaly inflow argument applied to intersecting D-branes and use this to determine the 8-form gravitational coupling.
507 citations
TL;DR: In this paper, it was shown that there is an arbitrary parameter which enters in the definition of the real connection, in the Poisson brackets, and therefore in the scale of the discrete spectra one finds for areas and volumes in the corresponding quantum theory.
Abstract: Both real and complex connections have been used for canonical gravity: the complex connection has SL(2,C) as the gauge group, while the real connection has SU(2) as the gauge group. We show that there is an arbitrary parameter which enters in the definition of the real connection, in the Poisson brackets, and therefore in the scale of the discrete spectra one finds for areas and volumes in the corresponding quantum theory. A value for could be singled out in the quantum theory by the Hamiltonian constraint or by the rotation to the complex Ashtekar connection.
450 citations
TL;DR: In this paper, the problem of gauge dependence in relativistic perturbation theory has been studied and the Taylor expansion of tensor fields under the action of one-parameter families (not necessarily groups) of diffeomorphisms is studied.
Abstract: We consider in detail the problem of gauge dependence that exists in relativistic perturbation theory, going beyond the linear approximation and treating second- and higher-order perturbations. We first derive some mathematical results concerning the Taylor expansion of tensor fields under the action of one-parameter families (not necessarily groups) of diffeomorphisms. Secondly, we define gauge invariance to an arbitrary order n. Finally, we give a generating formula for the gauge transformation to an arbitrary order and explicit rules to second and third order. This formalism can be used in any field of applied general relativity, such as cosmological and black hole perturbations, as well as in other spacetime theories. As a specific example, we consider here second-order perturbations in cosmology, assuming a flat Robertson - Walker background, giving explicit second-order transformations between the synchronous and the Poisson (generalized longitudinal) gauges.
349 citations
TL;DR: In this paper, the pair creation of (2 + 1)-dimensional black holes with event horizons of non-trivial topology is described and the spacetimes are all limiting cases of the cosmological C-metric.
Abstract: The pair creation of black holes with event horizons of non-trivial topology is described. The spacetimes are all limiting cases of the cosmological C-metric. They are generalizations of the (2 + 1)-dimensional black hole and have asymptotically anti-de Sitter behaviour. Domain wall instantons can mediate their pair creation for a wide range of mass and charge.
300 citations
TL;DR: In this paper, it was shown that equivalence classes of smooth or differentiable star products on a symplectic manifold M are parametrized by sequences of elements in the second de Rham cohomology space of the manifold.
Abstract: We give an elementary proof of the fact that equivalence classes of smooth or differentiable star products on a symplectic manifold M are parametrized by sequences of elements in the second de Rham cohomology space of the manifold. The parametrization is given explicitly in terms of Fedosov's construction which yields a star product when one chooses a symplectic connection and a sequence of closed 2-forms on M. We also show how derivations of a given star product, modulo inner derivations, are parametrized by sequences of elements in the first de Rham cohomology space of M.
196 citations
TL;DR: In this article, a Poincar e-gauge approach to gravity is used to construct ten possible distorted spacetimes, and the resulting solutions, appropriately matched to the distorted vacua, are interpreted as spin-polarized cosmic strings and cosmic dislocations.
Abstract: Cosmic strings, as topological spacetime defects, show striking resemblance to defects in solid continua: distortions, which can be classied into disclinations and dislocations, are linelike defects characterized by a delta function-valued curvature and torsion distribution giving rise to rotational and translational holonomy. We exploit this analogy and investigate how distortions can be adapted in a systematic manner from solid state systems to Einstein{Cartan gravity. As distortions are eciently described within the framework of a SO(3) T (3) gauge theory of solid continua with line defects, we are led in a straightforward way to a Poincar e gauge approach to gravity which is a natural framework for introducing the notion of distorted spacetimes. Constructing all ten possible distorted spacetimes, we recover, inter alia, the wellknown exterior spacetime of a spin-polarized cosmic string as a special case of such a geometry. In a second step, we search for matter distributions which, in Einstein{Cartan gravity, act as sources of distorted spacetimes. The resulting solutions, appropriately matched to the distorted vacua, are cylindrically symmetric and are interpreted as spin-polarized cosmic strings and cosmic dislocations.
193 citations
TL;DR: In this paper, it was shown that detectors with constant acceleration a in de Sitter (dS) and anti-de Sitter spaces with cosmological constants measure temperatures, and the existence of a thermal spectrum is also demonstrated for a variety of candidate wavefunctions in AdS backgrounds.
Abstract: We show, in complete accord with the usual Rindler picture, that detectors with constant acceleration a in de Sitter (dS) and anti-de Sitter (AdS) spaces with cosmological constants measure temperatures , the detector `5-acceleration' in the embedding flat 5-space. For dS, this recovers a known result; in AdS, where is negative, the temperature is well defined down to the critical value , again in accord with the underlying kinematics. The existence of a thermal spectrum is also demonstrated for a variety of candidate wavefunctions in AdS backgrounds.
187 citations
TL;DR: The Virgo gravitational wave detector is an interferometer with 3 km long arms in construction near Pisa to be commissioned in the year 2000 as mentioned in this paper, which is designed to achieve a strain sensitivity of a few times at 200 Hz.
Abstract: The Virgo gravitational wave detector is an interferometer with 3 km long arms in construction near Pisa to be commissioned in the year 2000. Virgo has been designed to achieve a strain sensitivity of a few times at 200 Hz. A large effort has gone into the conception of the mirror suspension system, which is expected to reduce noise to the level of at 10 Hz. The expected signals and main sources of noise are briefly discussed; the choices made are illustrated together with the present status of the experiment.
175 citations
TL;DR: The dynamical equations of an extended 1 + 3 orthonormal frame approach to the relativistic description of spacetime geometries are explicitly presented and discussed in detail in this article.
Abstract: The dynamical equations of an extended 1 + 3 orthonormal frame approach to the relativistic description of spacetime geometries are explicitly presented and discussed in detail In particular, the Bianchi identities for the Weyl curvature tensor occur in a fully expanded form, as they are given a central role in the extended formalism It is shown how one can naturally introduce local coordinates, both in the 1 + 3 threading and the ADM 3 + 1 slicing context By specializing the general 1 + 3 dynamical equations it is demonstrated how a number of problems of interest can be obtained In particular, the simplest choices of spatial frames for spatially homogeneous cosmological models, locally rotationally symmetric spacetime geometries, cosmological models with an Abelian isometry group and `silent' dust cosmological models are discussed
173 citations
TL;DR: The European Space Agency has selected LISA, a gravitational wave observatory, as a cornerstone mission in its future science program Horizons 2000 as mentioned in this paper, which will enable the observation of lowfrequency gravitational waves in a frequency range from 10−4 to 10−1 Hz which is totally inaccessible to ground-based experiments.
Abstract: The European Space Agency has selected LISA, a gravitational wave observatory, as a cornerstone mission in its future science program Horizons 2000. This observatory will complement the development of ground-based gravitational wave detectors currently under construction. A spaceborne detector will enable the observation of low-frequency gravitational waves in a frequency range from 10−4 to 10−1 Hz which is totally inaccessible to groundbased experiments. This frequency range is unique in that it is expected to contain signals from massive black holes, galactive binary stars, as well as the most violent events in the Universe. LISA will attain this low-frequency sensitivity by employing laser interferometric distance measurements over a very long baseline of 5 × 106 km. Three of these baselines form an equilateral triangle with spacecraft at each vertex. The cluster of spacecraft is in an Earth-like orbit around the Sun trailing the Earth by 20◦. The spacecraft contain infrared light-emitting Nd:YAG lasers and freely floating test masses made from a special platinum–gold alloy with vanishing magnetic susceptibility. The spacecraft are being kept centred on their test masses by using drag-free technology and field-emission electric propulsion, thus letting the test masses follow purely inertial orbits. PACS numbers: 0480N, 9555Y
TL;DR: In this paper, the authors apply the quantum-inequality-type restrictions to Alcubierre's warp drive metric on a scale in which a local region of spacetime can be considered "flat".
Abstract: We will apply the quantum-inequality-type restrictions to Alcubierre's warp drive metric on a scale in which a local region of spacetime can be considered `flat'. These are inequalities that restrict the magnitude and extent of the negative energy which is needed to form the warp drive metric. From this we are able to place limits on the parameters of the `warp bubble'. It will be shown that the bubble wall thickness is on the order of only a few hundred Planck lengths. Then we will show that the total integrated energy density needed to maintain the warp metric with such thin walls is physically unattainable.
TL;DR: In this paper, the authors revised their earlier rough estimate of the combined galactic and extragalactic binary confusion noise level curve for gravitational waves, allowing for roughly three frequency bins worth of information about weaker sources being lost for each galactic binary signal that is removed from the data.
Abstract: We have revised our earlier rough estimate of the combined galactic and extragalactic binary confusion noise level curve for gravitational waves. This was done to correct some numerical errors and to allow for roughly three frequency bins worth of information about weaker sources being lost for each galactic binary signal that is removed from the data. The results are still based on the spectral amplitude estimates for different types of galactic binaries reported by Hils et al in 1990, and assume that the gravitational wave power spectral densities for other galaxies are proportional to the optical luminosities. The estimated confusion noise level drops to the LISA instrumental noise level at between roughly 3 and 8 mHz.
TL;DR: The conformal equivalence between the Jordan and the Einstein frames can be used in order to search for exact solutions in general theories of gravity in which scalar fields are coupled with geometry in a standard or in a nonstandard way as discussed by the authors.
Abstract: The conformal equivalence between the Jordan and the Einstein frames can be used in order to search for exact solutions in general theories of gravity in which scalar fields are coupled with geometry in a standard or in a nonstandard way. In the cosmological arena a relevant role is played by the time parameter in which dynamics is described. In this paper we discuss the problem of conformal equivalence between a given nonstandard coupled model and the corresponding standard one. We analyse in detail the cosmological case and we see that, together with this, and through a careful analysis of the cosmological parameters and , it is possible to contribute to the discussion on which is the physical system.
TL;DR: In this article, it was shown that regions of negative energy density can undergo gravitational collapse into a black hole and the resultant exterior black hole spacetimes necessarily have negative mass and non-trivial topology.
Abstract: I demonstrate that, under certain circumstances, regions of negative energy density can undergo gravitational collapse into a black hole. The resultant exterior black hole spacetimes necessarily have negative mass and non-trivial topology. A full theory of quantum gravity, in which topology-changing processes take place, could give rise to such spacetimes.
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TL;DR: GEO600, an interferometric gravitational-wave detector with an arm length of 600 m, is currently being built in northern Germany close to Hannover as mentioned in this paper, where a master-slave combination of a monolithic diode-pumped Nd:YAG ring laser and an injection-locked amplifier will give a light power of about 10 W at a wavelength of 1064 nm.
Abstract: GEO600, an interferometric gravitational-wave detector with an arm length of 600 m, is currently being built in northern Germany close to Hannover. GEO600 incorporates an externally modulated fourfold delay-line Michelson interferometer giving a round-trip optical length of 2400 m. A master - slave combination of a monolithic diode-pumped Nd:YAG ring laser and an injection-locked amplifier will give a light power of about 10 W at a wavelength of 1064 nm. Power recycling increases the light power inside the interferometer to a level of about 10 kW. The use of both power and signal recycling will yield a sensitivity of the same order of magnitude as the first stages of the other large-scale gravitational-wave detectors LIGO and VIRGO currently under construction. High signal recycling factors allow the sensitivity to be increased at a chosen frequency while reducing the bandwidth of the detector. This gives an advantage over broad-band detectors in detecting narrow-band periodic sources such as pulsars. The 25 cm diameter mirrors will be suspended as double pendulums from a platform supported by vibration-reduction systems. The passive filtering properties of this system sufficiently reduce the seismic noise in the frequency range of interest, i.e. 50 - 1000 Hz. The detector will start taking data in the year 2000.
TL;DR: In this article, the authors argue that all superstring theories have more than one effective low-energy limit corresponding to classical spacetimes with different dimensionalities, and that all but the (3 + 1)-dimensional one might correspond to "dead worlds", devoid of observers, in which case all such ensemble theories would actually predict that we should find ourselves inhabiting a 3 + 1-dimensional spacetime.
Abstract: Some superstring theories have more than one effective low-energy limit corresponding to classical spacetimes with different dimensionalities. We argue that all but the (3 + 1)-dimensional one might correspond to `dead worlds', devoid of observers, in which case all such ensemble theories would actually predict that we should find ourselves inhabiting a (3 + 1)-dimensional spacetime. With more or less than one time dimension, the partial differential equations of nature would lack the hyperbolicity property that enables observers to make predictions. In a space with more than three dimensions, there can be no traditional atoms and perhaps no stable structures. A space with less than three dimensions allows no gravitational force and may be too simple and barren to contain observers.
TL;DR: In this article, a general-relativistic treatment of cosmological perturbations in a universe permeated by a large-scale primordial magnetic field using the Ellis - Bruni gauge-invariant formalism is provided.
Abstract: We provide a fully general-relativistic treatment of cosmological perturbations in a universe permeated by a large-scale primordial magnetic field using the Ellis - Bruni gauge-invariant formalism. The exact nonlinear equations for general-relativistic magnetohydrodynamic evolution are derived. A number of applications are made: the behaviour of small perturbations to Friedmann universes is studied; a comparison is made with earlier Newtonian treatments of cosmological perturbations and some effects of inflationary expansion are examined.
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TL;DR: In this article, the authors present a survey of recent results, scattered in a series of papers that have appeared during the past five years, whose common denominator has been the use of cubic relations in various algebraic structures.
Abstract: We present a survey of recent results, scattered in a series of papers that have appeared during the past five years, whose common denominator has been the use of cubic relations in various algebraic structures. Cubic (or ternary) relations can represent different symmetries with respect to the permutation group S3, or its cyclic subgroup Z3. Also ordinary or ternary algebras can be divided into different classes with respect to their symmetry properties. We pay special attention to the non-associative ternary algebra of 3-forms (or cubic matrices), and Z3-graded matrix algebras. We also discuss the Z3-graded generalization of Grassmann algebras and their realization in generalized exterior differential forms dξ and d2ξ, with d3ξ=0. A new type of gauge theory based on this differential calculus is presented. Finally, a ternary generalization of Clifford algebras is introduced, and an analogue of Dirac's equation is discussed, which can be diagonalized only after taking the cube of the Z3-graded generalization of Dirac's operator. A possibility of using these ideas for the description of quark fields is suggested and discussed in the last section.
TL;DR: For all dimensions and signatures, a symmetry operator for the massless Dirac equation can be constructed from a conformal Killing -Yano tensor of arbitrary degree in this paper.
Abstract: We show how, for all dimensions and signatures, a symmetry operator for the massless Dirac equation can be constructed from a conformal Killing - Yano tensor of arbitrary degree.
TL;DR: In this paper, the integrability conditions for the irrotational silent cosmological models were revisited and a series of constraint equations that need to be satisfied were formulated in 1 + 3 covariant and 1+ 3 orthonormal frame notation.
Abstract: We revisit the issue of integrability conditions for the irrotational silent cosmological models. We formulate the problem both in 1 + 3 covariant and 1 + 3 orthonormal frame notation and show that there exists a series of constraint equations that need to be satisfied. These conditions hold identically for FLRW-linearized silent models, but not in the general exact nonlinear case. Thus there is a linearization instability and it is highly unlikely that there is a large class of silent models. We conjecture that there are no spatially inhomogeneous solutions with Weyl curvature of Petrov type I and indicate further issues that await clarification.
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TL;DR: In this paper, a necessary and sufficient condition for these shift pairs to form a Lie algebra under the bracket operation induced by the Lie commutator of vector fields on spacetime was given.
Abstract: We study spacetime Killing vectors in terms of their `lapse and shift' relative to some spacelike slice. We give a necessary and sufficient condition in order for these lapse - shift pairs, which we call Killing initial data (KID), to form a Lie algebra under the bracket operation induced by the Lie commutator of vector fields on spacetime. This result is applied to obtain a theorem on the periodicity of orbits for a class of Killing vector fields in asymptotically flat spacetimes.
TL;DR: In this paper, the scalar-curvature action at the points of metric-degeneration is analyzed for a family of Morse-theory inspired cobordisms that vanish smoothly at a single point, resulting in a conical-type singularity there.
Abstract: We investigate topology change in (1 + 1) dimensions by analysing the scalar-curvature action at the points of metric-degeneration that (with minor exceptions) any non-trivial Lorentzian cobordism necessarily possesses. In two dimensions any cobordism can be built up as a combination of only two elementary types, the `yarmulke' and the `trousers.' For each of these elementary cobordisms, we consider a family of Morse-theory inspired Lorentzian metrics that vanish smoothly at a single point, resulting in a conical-type singularity there. In the yarmulke case, the distinguished point is analogous to a cosmological initial (or final) singularity, with the spacetime as a whole being obtained from one causal region of Misner space by adjoining a single point. In the trousers case, the distinguished point is a `crotch singularity' that signals a change in the spacetime topology (this being also the fundamental vertex of string theory, if one makes that interpretation). We regularize the metrics by adding a small imaginary part, whose sign is fixed to be positive by the condition that it lead to a convergent scalar field path integral on the regularized spacetime. As the regulator is removed, the scalar density approaches a delta-function, whose strength is complex: for the yarmulke family the strength is , where is the rapidity parameter of the associated Misner space; for the trousers family it is simply . This implies that in the path integral over spacetime metrics for Einstein gravity in three or more spacetime dimensions, topology change via a crotch singularity is exponentially suppressed, whereas appearance or disappearance of a universe via a yarmulke singularity is exponentially enhanced. We also contrast these results with the situation in a vielbein-cum-connection formulation of Einstein gravity.
TL;DR: In this paper, the local nature of Campbell's theorem is highlighted by studying the embedding of some lower-dimensional spaces, such as Ricci-flat spaces, and an embedding for the class of n-dimensional Einstein spaces.
Abstract: A little known theorem due to Campbell is employed to establish the local embedding of a wide class of four-dimensional spacetimes in five-dimensional Ricci-flat spaces. An embedding for the class of n-dimensional Einstein spaces is also found. The local nature of Campbell's theorem is highlighted by studying the embedding of some lower-dimensional spaces.
TL;DR: In this paper, a single auxiliary scalar field in a formulation with an infinite series of auxiliary (anti-) self-dual 5-form fields is constructed for the bosonic fields of D = 10 IIB supergravity.
Abstract: Covariant actions for the bosonic fields of D = 10 IIB supergravity are constructed with the help of a single auxiliary scalar field in a formulation with an infinite series of auxiliary (anti-)self-dual 5-form fields.
TL;DR: In this paper, it was shown that in the spherically symmetric case there are no black hole analogues of the regular boson star configurations, and the general no-hair theorem was then applied to the case of a theory that consists of a number of complex scalar fields minimally coupled to gravity that vary harmonically with time and has an arbitrary potential.
Abstract: We prove a general no-hair theorem which is then applied to the case of a theory that consists of a number of complex scalar fields minimally coupled to gravity that vary harmonically with time and has an arbitrary potential. This establishes that in the spherically symmetric case there are no black hole analogues of the regular boson star configurations.
TL;DR: In this paper, a formula for the Rovelli - Smolin volume operator is presented for the quantum configuration space of canonical gravity and compared with the quantum volume defined by Ashtekar and Lewandowski and a difference is indicated.
Abstract: The differential structure of the Ashtekar - Isham quantum configuration space of canonical gravity allows the expression of the operators, representing various geometrical objects, by compact analytic formulae. In this paper such a formula is presented for the Rovelli - Smolin volume operator. This operator is compared with the quantum volume defined by Ashtekar and Lewandowski and a difference is indicated.
TL;DR: In this paper, conformally covariant differential operators, which under local rescalings of the metric, transform according to for some r if is of order s, are discussed. And the flat space restrictions of their associated Green functions have forms which are strongly constrained by flat space conformal invariance.
Abstract: We discuss conformally covariant differential operators, which under local rescalings of the metric, , transform according to for some r if is of order s. It is shown that the flat space restrictions of their associated Green functions have forms which are strongly constrained by flat space conformal invariance. The same applies to the variation of the Green functions with respect to the metric. The general results are illustrated by finding the flat space Green function, and also its first variation, for previously found second-order conformal differential operators acting on k-forms in general dimensions. Furthermore, we construct a new second-order conformally covariant operator acting on rank-four tensors with the symmetries of the Weyl tensor whose Green function is similarly discussed. We also consider fourth-order operators, in particular a fourth-order operator acting on scalars in arbitrary dimension, which has a Green function with the expected properties. The results obtained here for conformally covariant differential operators are generalizations of standard results for the two-dimensional Laplacian on curved space and its associated Green function, which is used in the Polyakov effective gravitational action. It is hoped that they may have similar applications in higher dimensions.
TL;DR: In this article, the authors considered the field equations with G and both varying with time are considered in the context of general homogeneous, isotropic universes in a way which conserves the energy momentum tensor of the matter content.
Abstract: Einstein's field equations with G and both varying with time are considered in the context of general homogeneous, isotropic universes in a way which conserves the energy momentum tensor of the matter content. It is found that the solutions of the field equations, which are based on the variation of as but with different constants of proportionality, describe significantly different cosmological scenarios. It is also found that the non-static models with constant density having a vacuum-like equation of state are endowed with inflation for a wide class of functions G(t) and and a static universe with constant density without the vacuum-like equation of state, can exist only for k = 1 with constant G and .
TL;DR: In this article, a broad class of generalized gravity theories can be cast into Einstein gravity with a minimally coupled scalar field using a suitable conformal rescaling of the metric, using this conformal equivalence between the theories, derived the equations for the background and perturbations, and the general asymptotic solutions for the perturbation in the generalized gravity from the simple results known in the minimally-coupled scalar fields.
Abstract: A broad class of generalized gravity theories can be cast into Einstein gravity with a minimally coupled scalar field using a suitable conformal rescaling of the metric. Using this conformal equivalence between the theories, we derived the equations for the background and the perturbations, and the general asymptotic solutions for the perturbations in the generalized gravity from the simple results known in the minimally coupled scalar field. Results for the scalar and tensor perturbations can be presented in unified forms. The large-scale evolutions for both perturbations are characterized by corresponding conserved quantities. The simple result for the scalar perturbation is possible mainly due to our proper choice of a gauge-invariant combination which corresponds to the perturbed scalar field in the uniform-curvature gauge.