Showing papers in "Classical and Quantum Gravity in 2000"

Thermodynamics of Kerr-Newman-AdS black holes and conformal field theories

Abstract: We study the thermodynamics of four-dimensional Kerr-Newman-AdS black holes both in the canonical and the grand-canonical ensemble. The stability conditions are investigated, and the complete phase diagrams are obtained, which include the Hawking-Page phase transition in the grand-canonical ensemble. In the canonical case, one has a first-order transition between small and large black holes, which disappears for a sufficiently large electric charge or angular momentum. This disappearance corresponds to a critical point in the phase diagram. Via the AdS/CFT conjecture, the obtained phase structure is also relevant for the corresponding conformal field theory living in a rotating Einstein universe, in the presence of a global background U (1) current. An interesting limit arises when the black holes preserve some supersymmetry. These BPS black holes correspond to highly degenerate zero-temperature states in the dual CFT, which lives in an Einstein universe rotating with the speed of light.

Logarithmic corrections to black hole entropy, from the Cardy formula

Abstract: Many recent attempts to calculate black hole entropy from first principles rely on conformal field theory techniques. By examining the logarithmic corrections to the Cardy formula, I compute the first-order quantum correction to the Bekenstein-Hawking entropy in several models, including those based on asymptotic symmetries, horizon symmetries and certain string theories. Despite very different physical assumptions, these models all give a correction proportional to the logarithm of the horizon size, and agree qualitatively with recent results from `quantum geometry' in 3 + 1 dimensions. There are some indications that even the coefficient of the correction may be universal, up to differences that depend on the treatment of angular momentum and conserved charges.

Asymptotically anti-de Sitter spacetimes: conserved quantities

Abstract: Asymptotically anti-de Sitter spacetimes are considered in a general dimension d 4. As one might expect, the boundary conditions at infinity ensure that the asymptotic symmetry group is the anti-de Sitter group (although there is an interesting subtlety if d = 4). Asymptotic field equations imply that, associated with each generator of this group, there is a quantity Q which satisfies the expected `balance equation' if there is a flux of physical matter fields across the boundary at infinity and is absolutely conserved in the absence of this flux. Irrespective of the dimension d , all of these quantities vanish if the spacetime under considerations is (globally) anti-de Sitter. Furthermore, this result is required by a general covariance argument. However, it contradicts some of the recent findings based on the conjectured ADS/CFT duality. This and other features of our analysis suggest that, if a consistent dictionary between gravity and conformal field theories does exist in fully non-perturbative regimes, it would have to be more subtle than the one used currently.

Rotation sensing with a dual atom-interferometer Sagnac gyroscope

Abstract: We reports improvements to our Sagnac effect matter-wave interferometer gyroscope. This device now has a short-term rotation-rate sensitivity of 6×10−10 rad s−1 over 1 s of integration, which is the best publicly reported value to date. Stimulated Raman transitions are used to coherently manipulate atoms from counterpropagating thermal beams, forming two interferometers with opposite rotation phase shifts, allowing rotation to be distinguished from acceleration and laser arbitrary phase. Furthermore, electronically compensating the rotation-induced Doppler shifts of the Raman lasers allows operation at an effective zero rotation rate, improving sensitivity and facilitating sensitive lock-in detection readout techniques. Long-term stability is promising but not yet fully characterized. Potential applications include inertial navigation, geophysical studies and tests of general relativity.

A Lorentzian signature model for quantum general relativity

Abstract: We give a relativistic spin network model for quantum gravity based on the Lorentz group and its q-deformation, the Quantum Lorentz Algebra. We propose a combinatorial model for the path integral given by an integral over suitable representations of this algebra. This generalises the state sum models for the case of the four-dimensional rotation group previously studied in gr-qc/9709028. As a technical tool, formulae for the evaluation of relativistic spin networks for the Lorentz group are developed, with some simple examples which show that the evaluation is finite in interesting cases. We conjecture that the `10J' symbol needed in our model has a finite value.

General brane cosmologies and their global spacetime structure

Abstract: Starting from a completely general standpoint, we find the most general brane-universe solutions for a 3-brane in a five-dimensional spacetime. The brane can border regions of spacetime with or without a cosmological constant. Making no assumptions other than the usual cosmological symmetries of the metric, we prove that the equations of motion form an integrable system, and find the exact solution. The cosmology is indeed a boundary of a (class II) Schwarzschild-AdS spacetime, or a Minkowski (class I) spacetime. We analyse the various cosmological trajectories focusing particularly on those bordering vacuum spacetimes. We find, not surprisingly, that not all cosmologies are compatible with an asymptotically flat spacetime branch. We comment on the role of the radion in this picture.

Theorems on gravitational time delay and related issues

Abstract: Two theorems related to gravitational time delay are proven. Both theorems apply to spacetimes satisfying the null energy condition and the null generic condition. The first theorem states that if the spacetime is null geodesically complete, then given any compact set K, there exists another compact set K' such that for any p,qK', if there exists a `fastest null geodesic', γ, between p and q, then γ cannot enter K. As an application of this theorem, we show that if, in addition, the spacetime is globally hyperbolic with a compact Cauchy surface, then any observer at sufficiently late times cannot have a particle horizon. The second theorem states that if a timelike conformal boundary can be attached to the spacetime such that the spacetime with boundary satisfies strong causality as well as a compactness condition, then any `fastest null geodesic' connecting two points on the boundary must lie entirely within the boundary. It follows from this theorem that generic perturbations of anti-de Sitter spacetime always produce a time delay relative to anti-de Sitter spacetime itself.

A Brief review of 'little string theories'

Abstract: This is a brief review of the current state of knowledge on `little string theories', which are non-gravitational theories having several string-like properties. We focus on the six-dimensional maximally supersymmetric `little string theories' and describe their definition, some of their simple properties, the motivations for studying them, the discrete lightcone quantization and holographic constructions of these theories and their behaviour at finite energy density.

Diffeomorphisms and holographic anomalies

Abstract: Using the relation between diffeomorphisms in the bulk and Weyl transformations on the boundary, we study the Weyl transformation properties of the bulk metric on-shell and of the boundary action. We obtain a universal formula for one of the classes of trace anomalies in any even dimension in terms of the parameters of the gravity action.

Mechanics of isolated horizons

Abstract: A set of boundary conditions defining an undistorted, non-rotating isolated horizon are specified in general relativity. A spacetime representing a black hole which is itself in equilibrium but whose exterior contains radiation admits such a horizon. However, the definition is applicable in a more general context, such as cosmological horizons. Physically motivated, (quasi-)local definitions of the mass and surface gravity of an isolated horizon are introduced and their properties analysed. Although their definitions do not refer to infinity, these quantities assume their standard values in the static black-hole solutions. Finally, using these definitions, the zeroth and first laws of black-hole mechanics are established for isolated horizons.

Wilson loops in large-N theories

Abstract: We discuss how various aspects of Wilson loops in large-N gauge theories are studied from the point of view of the AdS-CFT correspondence.

Super-energy tensors

Abstract: A simple and purely algebraic construction of super-energy (s-e) tensors for arbitrary fields is presented in any dimensions. These tensors have good mathematical and physical properties, and they can be used in any theory having as basic arena an n-dimensional manifold with a metric of Lorentzian signature. In general, the completely timelike component of these s-e tensors has the mathematical features of an energy density: they are positive definite and satisfy the dominant property, which provides s-e estimates useful for global results and helpful in other matters, such as the causal propagation of the fields. Similarly, super-momentum vectors appear with the mathematical properties of s-e flux vectors. The classical Bel and Bel-Robinson tensors for the gravitational fields are included in our general definition. The energy-momentum and super-energy tensors of physical fields are also obtained, and the procedure will be illustrated by writing down these tensors explicitly for the cases of scalar, electromagnetic, and Proca fields. Moreover, higher order (super)k-energy tensors are defined and shown to be meaningful and in agreement for the different physical fields. In flat spacetimes, they provide infinitely many conserved quantities. In non-flat spacetimes, the fundamental question of the interchange of s-e quantities between different fields is addressed, and answered affirmatively. Conserved s-e currents are found for any minimally coupled scalar field whenever there is a Killing vector. Furthermore, the exchange of gravitational and electromagnetic super-energy is also shown by studying the propagation of discontinuities. This seems to open the door for new types of conservation physical laws.

The apparent shape of a rotating charged black hole, closed photon orbits and the bifurcation set A 4

Abstract: The apparent shapes of various Kerr-Newman spacetimes are plotted. For this purpose the geometry of closed photon orbits is studied, forming a subset of the bifurcation set A 4 , well known in elementary catastrophe theory. One additional result is that the cosmic censorship hypothesis guarantees that the spacetime casts a shadow, whereas naked ring singularities enable the visibility of the `anti-world' of negative radii r through its interior. Moreover, the optical restrictions to the observability of the shadow of an astronomical black hole are inferred.

Correlation functions of conserved currents in calN = 2 superconformal theory

Abstract: Using a manifestly supersymmetric formalism, we determine the general structure of two- and three-point functions of the supercurrent and the flavour current of = 2 superconformal field theories. We also express them in terms of = 1 superfields and compare to the generic = 1 correlation functions. A general discussion of the = 2 supercurrent superfield and the multiplet of anomalies and their definition as derivatives with respect to the supergravity prepotentials is also included.

The holographic principle for general backgrounds

Abstract: We aim to establish the holographic principle as a universal law, rather than a property only of static systems and special spacetimes. Our covariant formalism yields an upper bound on entropy which applies to both open and closed surfaces, independently of shape or location. It reduces to the Bekenstein bound whenever the latter is expected to hold, but complements it with novel bounds when gravity dominates. In particular, it remains valid in closed FRW cosmologies and in the interior of black holes. We give an explicit construction for obtaining holographic screens in arbitrary spacetimes (which need not have a boundary). This may aid the search for non-perturbative definitions of quantum gravity in spacetimes other than AdS. More details, references and examples can be found in papers by Bousso R (1999 J. High Energy Phys. JHEP07(1999)004, JHEP06(1999)028).

Scalar fields as dark matter in spiral galaxies

Abstract: We present a model for the dark matter in spiral galaxies, which is a result of a static and axial symmetric exact solution of the Einstein-dilaton theory. We suppose that dark matter is a scalar field endowed with a scalar potential. We obtain that (a) the effective energy density goes like 1/(r 2 +rc 2 ) and (b) the resulting circular velocity profile of test particles is in good agreement with the observed one.

Quintessence and scalar dark matter in the universe

Abstract: Continuing on from previous works, we present a cosmological model in which dark matter and dark energy are modelled by scalar fields Φ and Ψ, respectively, endowed with the scalar potentials V(Φ) = Vo[cosh (λ√κoΦ) - 1] and (Ψ) = o[sinh (α√κoΨ)]β. This model contains a 95% scalar field. We obtain that the scalar dark matter mass is mΦ~10-26 eV. The solution obtained allows us to recover the success of standard cold dark matter. The implications on the formation of structure are reviewed. We obtain that the minimal cut-off radio for this model is rc ~ 1.2 kpc.

Scalar fields, energy conditions and traversable wormholes

Abstract: We describe the different possibilities that a simple and apparently quite harmless classical scalar field theory provides to violate the energy conditions. We demonstrate that a non-minimally coupled scalar field with a positive curvature coupling ξ>0 can easily violate all the standard energy conditions, up to and including the averaged null energy condition (ANEC). Indeed, this violation of the ANEC suggests the possible existence of traversable wormholes supported by non-minimally coupled scalars. To investigate this possibility we derive the classical solutions for gravity plus a general (arbitrary ξ) massless non-minimally coupled scalar field, restricting attention to the static and spherically symmetric configurations. Among these classical solutions we find an entire branch of traversable wormholes for every ξ>0. (This includes and generalizes the case of conformal coupling ξ = (1/6) we considered in 1999 Phys. Lett. B 466 127-34.) For these traversable wormholes to exist we demonstrate that the scalar field must reach trans-Planckian values somewhere in the geometry. We discuss how this can be accommodated within the current state of the art regarding scalar fields in modern theoretical physics. We emphasize that these scalar field theories, and the traversable wormhole solutions we derive, are compatible with all known experimental constraints from both particle physics and gravity.

Black string instabilities in anti-de Sitter space

Abstract: We show how to extend the usual black string instability of vacuum or charged black p-branes to the anti-de Sitter background. The string fragments in an analogous fashion to the Λ = 0 case, the main difference being that instead of a periodic array of black holes forming, an accumulation of `mini' black holes occurs towards the AdS horizon. In the case where the AdS space is of finite extent, such as an orbifold compactification, we show how the instability switches off below a certain compactification scale.

Gupta-Bleuler quantization for minimally coupled scalar fields in de Sitter space

Abstract: We present a fully covariant quantization of the minimally coupled massless field on de Sitter space, thanks to a new representation of the canonical commutation relations. We thus obtain a formalism free of any infrared divergence. Our method is based on a rigorous group-theoretical approach combined with a suitable adaptation (Krein spaces) of the Wightman-Garding axiomatic for massless fields (Gupta-Bleuler scheme). We make explicit the correspondence between unitary irreducible representations of the de Sitter group and the field theory on de Sitter spacetime. The minimally coupled massless field is associated with a representation which is the lowest term of the discrete series of unitary representations of the de Sitter group. In spite of the presence of negative-norm modes in the theory, no negative energy can be measured: expressions such as n k 1 n k 2 ... |T 00 |n k 1 n k 2 ... are always positive.

Scalar field as dark matter in the universe

Abstract: We investigate the hypothesis that the scalar field is the dark matter and the dark energy in the cosmos, which comprises about 95% of the matter of the Universe. We show that this hypothesis explains quite well the recent observations on type Ia supernovae.

A study of angular size-redshift relation for models in which Λ decays as the energy density

Abstract: By modifying the Chen and Wu ansatz, we have investigated some Friedmann models in which Λ varies as ρ. In order to test the consistency of the models with observations, we study the angular size-redshift relation for 256 ultracompact radio sources selected by Jackson and Dodgson. The angular sizes of these sources were determined by using very long-baseline interferometry in order to avoid any evolutionary effects. The models fit the data very well and require an accelerating universe with a positive cosmological constant. Open, flat and closed models are almost equally probable, though the open model provides a comparatively better fit to the data. The models are found to have intermediate density and imply the existence of dark matter, though not as much as in the canonical Einstein-de Sitter model.

A general worldline quantum inequality

Abstract: Worldline quantum inequalities provide lower bounds on weighted averages of the renormalized energy density of a quantum field along the worldline of an observer. In the context of real, linear scalar field theory on an arbitrary globally hyperbolic spacetime, we establish a worldline quantum inequality on the normal ordered energy density, valid for arbitrary smooth timelike trajectories of the observer, arbitrary smooth compactly supported weight functions and arbitrary Hadamard quantum states. Normal ordering is performed relative to an arbitrary choice of Hadamard reference states. The inequality obtained generalizes a previous result derived for static trajectories in a static spacetime. The underlying argument is straightforward and is made rigorous using the techniques of microlocal analysis. In particular, an important role is played by the characterization of Hadamard states in terms of the microlocal spectral condition. We also give a compact form of our result for stationary trajectories in a stationary spacetime.

Theory and phenomenology of type I strings and M-theory

Abstract: The physical motivations and the basic construction rules for type I strings and M-theory compactifications are reviewed in the light of recent developments. The first part of this review contains the basic theoretical ingredients needed for building four-dimensional supersymmetric models, models with broken supersymmetry, and for computing low-energy actions and quantum corrections to these. The second part contains some phenomenological applications to brane world scenarios with low values of the string scale and large extra dimensions.

Fuchsian analysis of singularities in Gowdy spacetimes beyond analyticity

Abstract: Fuchsian equations provide a way of constructing large classes of spacetimes whose singularities can be described in detail. In some of the applications of this technique only the analytic case could be handled up to now. This paper develops a method of removing the undesirable hypothesis of analyticity. This is applied to the specific case of the Gowdy spacetimes in order to show that analogues of the results known in the analytic case hold in the smooth case. As far as possible the likely strengths and weaknesses of the method, as applied to more general problems, are displayed.

SO(4,C)-covariant Ashtekar-Barbero gravity and the Immirzi parameter

Abstract: An so(4,C)-covariant Hamiltonian formulation of a family of generalized Hilbert-Palatini actions depending on a parameter (the so-called Immirzi parameter) is developed. It encompasses the Ashtekar-Barbero gravity which serves as a basis of quantum loop gravity. Dirac quantization of this system is constructed. Next we study the dependence of the quantum system on the Immirzi parameter. The path-integral quantization shows no dependence on it. A method of modifying the loop approach in accordance with the formalism developed here is briefly outlined.

Non-BPS D-branes in string theory

Abstract: In this paper I shall discuss some aspects of non-BPS D-branes in string theory. PACS number: 1125

Supersymmetry of topological Kerr-Newman-Taub- NUT-adS spacetimes

Abstract: We extend the topological Kerr-Newman-adS solutions by including NUT charge and find generalizations of the Robinson-Bertotti solution to the negative cosmological constant case with different topologies. We show how all of these solutions can be obtained as limits of the general Plebanski-Demianski solution. We study the supersymmetry properties of all these solutions in the context of gauged N = 2, d = 4 supergravity. Generically they preserve, at most, quarter of the total supersymmetry. In the Plebanski-Demianski case, although gauged N = 2, d = 4 supergravity does not have electro-magnetic duality, we find that the family of supersymmetric solutions still exhibits an electro-magnetic duality in which electric and magnetic charges and mass and Taub-NUT charge are rotated simultaneously.

Symmetry reduction for quantized diffeomorphism-invariant theories of connections

Abstract: Given a symmetry group acting on a principal fibre bundle, symmetric states of the quantum theory of a diffeomorphism-invariant theory of connections on this fibre bundle are defined These symmetric states, equipped with a scalar product derived from the Ashtekar-Lewandowski measure for loop quantum gravity, form a Hilbert space of their own Restriction to this Hilbert space yields a quantum symmetry reduction procedure within the framework of spin-network states, the structure of which is analysed in detail Three illustrating examples are discussed: reduction of (3+1)- to (2+1)-dimensional quantum gravity, spherically symmetric quantum electromagnetism and spherically symmetric quantum gravity In the latter system the eigenvalues of the area operator applied to the spherically symmetric spin-network states have the form An(n(n + 2))1/2, n = 0,1,2,, giving Ann for large n This result clarifies (and reconciles) the relationship between the more complicated spectrum of the general (non-symmetric) area operator in loop quantum gravity and the old Bekenstein proposal that Ann

Curvature blow up in Bianchi VIII and IX vacuum spacetimes

Abstract: The maximal globally hyperbolic development of non-Taub-NUT Bianchi IX vacuum initial data and of non-NUT Bianchi VIII vacuum initial data is C-2-inextendible. Furthermore, a curvature invariant is unbounded in the incomplete directions of inextendible causal geodesics.