We construct solutions for thin black rings in Anti-deSitter and deSitter spacetimes using approximate methods. Black rings in AdS exist with arbitrarily large radius and satisfy a bound |J| \leq LM, which they saturate as their radius becomes infinitely large. For angular momentum near the maximum, they have larger area than rotating AdS black holes. Thin black rings also exist in deSitter space, with rotation velocities varying between zero and a maximum, and with a radius that is always strictly below the Hubble radius. Our general analysis allows us to include black Saturns as well, which we discuss briefly. We present a simple physical argument why supersymmetric AdS black rings must not be expected: they do not possess the necessary pressure to balance the AdS potential. We discuss the possible existence or absence of `large AdS black rings' and their implications for a dual hydrodynamic description. An analysis of the physical properties of rotating AdS black holes is also included.
For asymptotically flat spacetimes the Penrose inequality gives an initial data test for the weak cosmic censorship hypothesis. We give a formulation of this inequality for asymptotically anti-deSitter (AAdS) spacetimes, and show that the inequality holds for time asymmetric data in spherical symmetry. Our analysis is motivated by the constant-negative-spatial-curvature form of the AdS black hole metric.
At low energy the near horizon geometry of nonextreme black holes in four dimensions exhibits an effective SL(2,R)_L x SL(2,R)_R symmetry. The parameters of the corresponding induced conformal field theory gives the correct expression for the black hole entropy. The resulting spectrum of the Schwarzchild black hole is compared with another proposal.
We express the Noether charge entropy density of a black brane in anti-deSitter space in terms of local operators in the anti-deSitter space bulk. We find that Wald's expression for the Noether charge entropy needs to be modified away from the horizon by an additional term that vanishes on the horizon. We then determine the field theory dual of the Noether charge entropy for theories that asymptote to Einstein theory. We do so by calculating the value of the entropy density at the anti-deSitter space boundary and applying the standard rules of the AdS/CFT correspondence. We interpret the varia…
We study a solution of the Einstein's equations generated by a self-gravitating, anisotropic, static, non-singular matter fluid. The resulting Schwarzschild like solution is regular and accounts for smearing effects of noncommutative fluctuations of the geometry. We call this solution regular Schwarzschild spacetime. In the presence of an Anti-deSitter cosmological term, the regularized metric offers an extension of the Hawking-Page transition into a van der Waals-like phase diagram. Specifically the regular Schwarzschild-Anti-deSitter geometry undergoes a first order small/large black hole tr…
Quantum field theory on d+1-dimensional anti-deSitter space-time admits a re-interpretation as a quantum field theory with conformal symmetry on d-dimensional Minkowski space-time. This conjecture originally emerged from string theory considerations. Here, it is proven in a general framework by an explicit identification between the local observables of the two corresponding theories.
We describe a formalism for studying spherically symmetric collapse of the massless scalar field in any spacetime dimension, and for any value of the cosmological constant $Λ$. The formalism is used for numerical simulations of gravitational collapse in four spacetime dimensions with negative $Λ$. We observe critical behaviour at the onset of black hole formation, and find that the critical exponent is independent of $Λ$.
In this paper we present the construction of the Maxwell equal area law in the Hawking temperature graph for a charged black hole in Anti-deSitter background. We are able to find exact solution for the corresponding isotherm and entropies for "gaseous" (large) black holes and "liquid" (near-extremal) black holes. Isothermal construction removes the unphysical, negative heat capacity, regions. Furthermore, extremal black holes turn out to be dual to "un-shrinkable" molecules of Van der Waals real fluid, which may explain their thermodynamical stability.
A model for a flat isotropic universe with a negative cosmological constant $Λ$ and a massless scalar field as sole matter content is studied within the framework of Loop Quantum Cosmology. By application of the methods introduced for the model with $Λ=0$, the physical Hilbert space and the set of Dirac observables are constructed. As in that case, the scalar field plays here the role of an emergent time. The properties of the system are found to be similar to those of the $k=1$ FRW model: for small energy densities, the quantum dynamics reproduces the classical one, whereas, due to modificati…
We prove the existence of one quarter supersymmetric type IIB configurations that arise as non-trivial scaling solutions of the standard five dimensional Kerr-AdS black holes by the explicit construction of its Killing spinors. This neutral, spinning solution is asymptotic to the static anti-deSitter space-time with cosmological constant $-\textstyle{\frac{1}{\ell^2}}$, it has two finite equal angular momenta $J_1=\pm J_2$, mass $M=\textstyle{\frac{1}{\ell}} (|J_1|+|J_2|)$ and a naked singularity.We also address the scaling limit associated with one half supersymmetric solution with only one a…
A rigorous (and simple) proof is given that there is a one-to-one correspondence between causal anti-deSitter covariant quantum field theories on anti-deSitter space and causal conformally covariant quantum field theories on its conformal boundary. The correspondence is given by the explicit identification of observables localized in wedge regions in anti-deSitter space and observables localized in double-cone regions in its boundary. It takes vacuum states into vacuum states, and positive-energy representations into positive-energy representations.
We study the problem of a Schwarzschild-anti-deSitter black hole in a noncommutative geometry framework, thought to be an effective description of quantum-gravitational spacetime. As a first step we derive the noncommutative geometry inspired Schwarzschild-anti-deSitter solution. After studying the horizon structure, we find that the curvature singularity is smeared out by the noncommutative fluctuations. On the thermodynamics side, we show that the black hole temperature, instead of a divergent behavior at small scales, admits a maximum value. This fact implies an extension of the Hawking-Pag…
Understanding transitions between different vacua of a multiverse allowing eternal inflation is an open problem whose resolution is important to gain insights on the global structure of the spacetime as well as the problem of measure. In the classical theory, transitions from the anti-deSitter to deSitter vacua are forbidden due to the big crunch singularity. In this article, we consider toy landscape potentials: a double well and a triple well potential allowing anti-deSitter and de-Sitter vacua, in the effective dynamics of loop quantum cosmology for the $k=-1$ FRW model. We show that due to…
We investigate the charged Schwarzschild-Anti-deSitter (SAdS) BH thermodynamics in 5d Einstein-Gauss-Bonnet gravity with electromagnetic field. The Hawking-Page phase transitions between SAdS BH and pure AdS space are studied. The corresponding phase diagrams (with critical line defined by GB term coefficient and electric charge) are drawn. The possibility to account for higher derivative Maxwell terms is mentioned. In frames of proposed dS/CFT correspondence it is demonstrated that brane gravity maybe localized similarly to AdS/CFT. SdS BH thermodynamics in 5d Einstein and Einstein-Gauss-Bonn…
A deSitter brane-world bounding regions of anti-deSitter space has a macroscopic entropy given by one-quarter the area of the observer horizon. A proposed variant of the AdS/CFT correspondence gives a dual description of this cosmology as conformal field theory coupled to gravity in deSitter space. In the case of two-dimensional deSitter space this provides a microscopic derivation of the entropy, including the one-quarter, as quantum entanglement of the conformal field theory across the horizon.
The problem of perturbative breakdown of conformal symmetry can be avoided, if a conformally covariant quantum field phi on d-dimensional Minkowski spacetime is viewed as the boundary limit of a quantum field Phi on d+1-dimensional anti-deSitter spacetime (AdS). We study the boundary limit in renormalized perturbation theory with polynomial interactions in AdS, and point out the differences as compared to renormalization directly on the boundary. In particular, provided the limit exists, there is no conformal anomaly. We compute explicitly the "fish diagram" on AdS_4 by differential renormaliz…
Gravitational perturbations of anti-deSitter spacetime play important roles in AdS/CFT correspondence and the brane world scenario. In this paper, we develop a gauge-invariant formalism of gravitational perturbations of maximally symmetric spacetimes including anti-deSitter spacetime. Existence of scalar-type master variables is shown and the corresponding master equations are derived.
Compactifications of type IIB string theory on AdS5 x X5, where X5 is an Einstein space, can have one-fourth or half maximal supersymmetry for certain choices of X5. Some of these theories admit exotic domain walls arising from 5-branes wrapping 2-cycles in X5. We explore the relationship among these domain walls, fractional branes and branes stretched on intervals. World-volume fluxes in the wrapped branes play an important role in the analysis. We draw some parallels between the AdS background with exotic domain walls and N=1 supersymmetric MQCD, and identify other extended objects on the Ad…
We study classes of five-dimensional cosmological solutions with negative curvature, which are obtained from static solutions by an exchange of a spatial and temporal coordinate, and in some cases by an analytic continuation. Such solutions provide a suitable laboratory to address the time-dependent AdS/CFT correspondence. For a specific example we address in detail the calculation of the boundary stress-energy and the Wilson line and find disagreement with the standard AdS/CFT correspondence. We trace these discrepancies to the time-dependent effects, such as particle creation, which we furth…
We investigate supersymmetric extrema of Abelian gauged supergravity theories with non-trivial vector multiplets and 8 supercharges in four and five dimensions. The scalar fields of these models parameterize a manifold consisting of disconnected branches and restricting to the case where this manifold has a non-singular metric we show that on every branch there can be at most one extremum, which is a local maximum (for W>0) or a minimum (for W<0) of the superpotential W. Therefore, these supergravity models do not allow for regular domain wall solutions interpolating between different extrema …
We argue that flat space amplitudes for the process $ 2 \to n$ gravitons at center of mass energies $\sqrt{s}$ much less than the Planck scale, will coincide approximately with amplitudes calculated from correlators of a boundary CFT for AdS space of radius $R\gg L_P$, only when $n < R/L_P$ . For larger values of $n$ in AdS space, insisting that all the incoming energy enters "the arena" [arXiv:hep-th/9901079], implies the production of black holes, whereas there is no black hole production in the flat space amplitudes. We also argue, from unitarity, that flat space amplitudes for all $n$ are …
A novel method, based on superpotentials is proposed for obtaining the quasi-normal modes of anti-de Sitter black holes. This is inspired by the case of the three-dimensional BTZ black hole, where the quasi-normal modes can be obtained exactly and are proportional to the surface gravity. Using this approach, the quasi-normal modes of the five dimensional Schwarzschild anti-deSitter black hole are computed numerically. The modes again seem to be proportional to the surface gravity for very small and very large black holes. They reflect the well-known instability of small black holes in anti-deS…
It is natural to analyse the AdS$_{d+1}$-CQFT$_{d}$ correspondence in the context of the conformal- compactification and covering formalism. In this way one obtains additional inside about Rehren's rigorous algebraic holography in connection with the degree of freedom issue which in turn allows to illustrates the subtle but important differences beween the original string theory-based Maldacena conjecture and Rehren's theorem in the setting of an intrinsic field-coordinatization-free formulation of algebraic QFT. I also discuss another more generic type of holography related to light fronts wh…
We study the constraints on HST models of AdS space-time. The causal diamonds of HST along time-like geodesics of AdS space-time, fit nicely into the FRW patch of AdS space. The coordinate singularity of the FRW patch is identified with the proper time at which the Hilbert space of the causal diamond becomes infinite dimensional. For diamonds much smaller than the AdS radius, RAdS, the time dependent Hamiltonians of HST are the same as those used to describe similar diamonds in Minkowski space. In particular, they are invariant under the fuzzy analog of volume preserving diffeomorphisms of the…
The dS/CFT correspondence differs from its AdS/CFT counterpart in some ways, yet is strikingly similar to it in many others. For example, both involve CFTs defined on connected spaces (despite the fact that the conformal boundary of deSitter space is not connected), and both impose constraints on scalar masses (Strominger's bound for deSitter, and the Breitenlohner-Freedman bound for Anti-deSitter). We argue that these similarities can be explored and exploited using a slight extension of the Euclidean approach to AdS/CFT. The methods are particularly compatible with Hull's embedding of deSitt…
We construct asymptotically anti-deSitter (and deSitter) black hole solutions of Einstein-Born-Infeld theory in arbitrary dimension. We critically analyse their geometries and discuss their thermodynamic properties.
We consider a model with two parallel (positive tension) 3-branes separated by a distance $L$ in 5-dimensional spacetime. If the interbrane space is anti-deSitter, or is not precisely anti-deSitter but contains no event horizons, the effective 4-dimensional cosmological constant seen by observers on one of the branes (chosen to be the visible brane) becomes exponentially small as $L$ grows large.
We investigate the Schwarzschild-Anti-deSitter (SAdS) and SdS BH thermodynamics in 5d higher derivative gravity. The interesting feature of higher derivative gravity is the possibility for negative (or zero) SdS (or SAdS) BH entropy which depends on the parameters of higher derivative terms. The appearence of negative entropy may indicate a new type instability where a transition between SdS (SAdS) BH with negative entropy to SAdS (SdS) BH with positive entropy would occur or where definition of entropy should be modified.
String theory is arguably the best candidate for a theory of quantum gravity and unified interactions. Reconciling Einstein's theory of General Relativity with Quantum Mechanics. The theory however is best understood on Minkowski and Anti-de Sitter space-times, and not on exponentially expanding space-times with positive cosmological constant, like our own universe. There is still no satisfactory formulation of String Theory on these so called asymptotically de Sitter space times. In this thesis I will discuss certain avenues of progress towards a String Theory formulation of de Sitter space-t…
Recently our understanding of black holes in D-spacetime dimensions, as solutions of the Einstein equation, has advanced greatly. Besides the well established spherical black hole we have now explicitly found other species of topologies of the event horizons. Whether in asymptotically flat, AntideSitter or deSitter spaces, the different species are really non-unique when D > 4. An example of this are the black rings. Another issue in higher dimensions that is not fully understood is the struggle for existence of regular black hole solutions. However, we managed to observe a selection rule for …
We study a deSitter/Anti-deSitter/Poincare Yang-Mills theory of gravity in d-space-time dimensions in an attempt to retain the best features of both general relativity and Yang-Mills theory: quadratic curvature, dimensionless coupling and background independence. We derive the equations of motion for Lie algebra valued scalars and show that in the geometric optics limit they traverse geodesics with respect to the Lorentzian geometry determined by the frame fields. Mixing between components appears to next to leading order in the WKB approximation. We then restrict to two space-time dimensions …
We study topology-changing transitions in the space of higher-dimensional black hole solutions. Kol has proposed that these are conifold-type transitions controlled by self-similar double-cone geometries. We present an exact example of this phenomenon in the intersection between a black hole horizon and a cosmological deSitter horizon in D >= 6. We also describe local models for the critical geometries that control many transitions in the phase space of higher-dimensional black holes, such as the pinch-down of a topologically spherical black hole to a black ring or to a black p-sphere, or the …
A uniformly acclerated observer in anti-deSitter space-time is known to detect thermal radiation when the acceleration exceeds a critical value. We investigate the holographic interpretation of this phenomenon. For uniformly accelerated trajectories transverse to the boundary of the AdS space, the hologram is a blob which expands along the boundary. Observers on the boundary co-moving with the hologram become observers in cosmological space-times. For supercritical accelerations one gets a Milne universe when the holographic screen is the boundary in Poincare coordinates, while for the boundar…
Time-symmetric initial data for two-body solutions in three dimensional anti-deSitter gravity are found. The spatial geometry has constant negative curvature and is constructed as a quotient of two-dimensional hyperbolic space. Apparent horizons correspond to closed geodesics. In an open universe, it is shown that two black holes cannot exist separately, but are necessarily enclosed by a third horizon. In a closed universe, two separate black holes can exist provided there is an additional image mass.
We prove that five-dimensional extreme anti-de Sitter black ring solutions to the vacuum Einstein equations that admit biaxial symmetry do not exist. This is established by demonstrating the nonexistence of five-dimensional, biaxisymmetric, vacuum near-horizon geometries of extreme horizons with a nonzero cosmological constant and ring topology.
We shall first discuss motivation for higher dimension even for classical description of gravitational dynamics and then construct a black hole out of an anti-deSitter (AdS) spacetime by prescribing a coupling between Gauss-Bonnet parameter, constant curvature of extra dimensional space and $Λ$. This is a creation of pure curvature which establishes the fundamental reciprocity between matter and gravity/curvature.
We demonstrate that $(D+1)$-dimensional, locally asymptotically anti-deSitter spacetimes with nonzero NUT charge generically do not respect the usual relationship between area and entropy. This result does not depend on either the existence of closed timelike curves nor on the removal of Misner string singularities, but instead is a consequence of the first law of thermodynamics.
We construct five dimensional black rings in global anti-de Sitter space using numerical methods. These rings satisfy the BPS bound $| J | < M \ell$, but the angular velocity always violates the Hawking-Reall bound $| Ω_H \ell | \leq 1$, indicating that they should be unstable under superradiance. At high temperatures, the limit $| Ω_H \ell | \searrow 1$ is attained by thin rings with an arbitrarily large radius. However, at sufficiently low temperatures, this limit is saturated by a new kind of rings, whose outer circle can still be arbitrarily long while the hole in the middle does not grow …
It is generally believed the way to resolve the black hole information paradox in string theory is to embed the black hole in anti-deSitter spacetime -- without of course claiming that Schwarzschild-AdS is a realistic spacetime. Here we propose that, similarly, the best way to study topologically non-trivial versions of de Sitter spacetime from a stringy point of view is to embed them in an anti-de Sitter orbifold bulk, again without claiming that this is literally how de Sitter arises in string theory. Our results indicate that string theory may rule out the more complex spacetime topologies …
We show that a class of four-dimensional rotating black holes allow five-dimensional embeddings as black rotating strings. Their near-horizon geometry factorizes locally as a product of the three-dimensional anti-deSitter space-time and a two-dimensional sphere (AdS_3 x S^2), with angular momentum encoded in the global space-time structure. Following the observation that the isometries on the AdS_3 space induce a two-dimensional (super)conformal field theory on the boundary, we reproduce the microscopic entropy with the correct dependence on the black hole angular momentum.
We determine the most general near-horizon geometry of a supersymmetric, asymptotically anti-de Sitter, black hole solution of five-dimensional minimal gauged supergravity that admits two rotational symmetries. The near-horizon geometry is that of the supersymmetric, topologically spherical, black hole solution of Chong et al. This proves that regular supersymmetric anti-de Sitter black rings with two rotational symmetries do not exist in minimal supergravity. However, we do find a solution corresponding to the near-horizon geometry of a supersymmetric black ring held in equilibrium by a conic…
We investigated the evolution of a scalar field propagating in small Schwarzschild Anti-de Sitter black holes. The imaginary part of the quasinormal frequency decreases with the horizon size and the real part of the quasinormal frequency keeps nearly as a constant. The object-picture clarified the question on the quasinormal modes for small Anti-de Sitter black holes. Dependence of quasinormal modes on spacetime dimensions and the multipole index for small Anti-de Sitter black holes have also been illustrated.
In this paper, we survey the nature of spinors and supersymmetry (SUSY) in various types of spaces. We treat two distinct types of spaces: flat spaces and spaces of constant (non-zero) curvature. The flat spaces we consider are either three or four dimensional of signatures 3 + 1, 4 + 0, 2 + 2 and 3 + 0. In each of these cases, SUSY generators anti-commute to yield the generators of translations in the non-compact flat spaces. The spaces of constant curvature we consider are two-dimensional: the surface of the sphere S_2 and the Anti-deSitter space AdS_2. S_2 is embedded in a 3 + 0 Euclidean s…
We consider 5-dimensional Einstein-dilaton gravity with antisymmetric forms. Assuming staticity and a restriction on the dilaton coupling parameters, we derive 4-dimensional sigma-model with a target space $SL(2,R)/SO(1,1)\times SL(2,R)/SO(1,1)$. On this basis, using the symmetries of the target space, we develop a solution generating technique and employ it to construct new asymptotically flat and non-flat dyonic black rings solutions. The solutions are analyzed and the basic physical quantities are calculated.
A recent study of supersymmetric domain walls in $N=1$ supergravity theories revealed a new class of domain walls interpolating between supersymmetric vacua with different non-positive cosmological constants. We classify three classes of domain wall configurations and study the geodesic structure of the induced space-time. Motion of massive test particles in such space-times shows that these walls are always repulsive from the anti-deSitter (AdS) side, while on the Minkowski side test particles feel no force. Freely falling particles far away from a wall in an AdS vacuum experience a constant …
