Schwarzschild Anti-de Sitter Research Articles

Alpha-vacua, black holes and AdS/CFT

The Schwarzschild, Schwarzschild–AdS and Schwarzschild–de Sitter solutions all admit freely acting discrete involutions which commute with the continuous symmetries of the spacetimes. Intuitively, these involutions correspond to the antipodal map of the corresponding spacetimes. In analogy with the ordinary de Sitter example, this allows us to construct new vacua by performing a Mottola–Allen transform on the modes associated with the Hartle–Hawking, or Euclidean, vacuum. These vacua are the ‘alpha’-vacua for these black holes. The causal structure of a typical black hole may ameliorate certain difficulties which are encountered in the case of de Sitter α-vacua. For Schwarzschild–AdS black holes, a Bogoliubov transformation which mixes operators of the two boundary CFT's provides a construction of the dual CFT α-states. Finally, we analyse the thermal properties of these vacua.

Strong interactions and gauge-string duality

We discuss some recent phenomenological models for strong interactions based on the idea of gauge/string duality. A very good estimate for hadronic masses can be found by placing an infrared cut off in AdS space. Considering static strings in this geometry one can also reproduce the phenomenological Cornell potential for a quark anti-quark pair at zero temperature. Placing static strings in an AdS Schwarzschild space with an infrared cut off one finds a transition from a confining to a deconfining phase at some critical horizon radius (associated with temperature).

Asymptotically hyperbolic metrics on the unit ball with horizons

In this paper, we construct a family of three-dimensional asymptotically hyperbolic manifolds with horizons and with scalar curvature equal to −6. The manifolds we construct can be arbitrarily close to anti-de Sitter-Schwarzschild manifolds at infinity. Hence, the mass of our manifolds can be very large or very small. The main arguments we use in this paper are gluing methods which are used by Miao in (Proc Am Math Soc 132(1):217–222, 2004).

Electromagnetic quasinormal modes of D-dimensional black holes

Using the monodromy method we calculate the asymptotic quasinormal frequencies of an electromagnetic field moving in D-dimensional Schwarzschild and Schwarzschild de Sitter black holes (D ≥ 4). For the D-dimensional Schwarzschild anti-de Sitter black hole we also compute these frequencies with a similar method. Moreover, we calculate the electromagnetic normal modes of the D-dimensional anti-de Sitter spacetime.

Braneworld stars and black holes

We look for spherically symmetric star or black hole solutions on a Randall–Sundrum brane from the perspective of the bulk. We take a known bulk solution, and analyse possible braneworld trajectories within it that correspond, from the braneworld point of view, to solutions of the brane Tolman–Oppenheimer–Volkoff equations. Our solutions are therefore embedded consistently into a full bulk solution. We find the full set of static gravitating matter sources on a brane in a range of bulk spacetimes, analysing which can correspond to physically sensible sources. Finally, we look at time-dependent trajectories in a Schwarzschild–anti-de Sitter spacetime as possible descriptions of time-dependent braneworld black holes, highlighting some of the general features one might expect, as well as some of the difficulties involved in getting a full solution to the question.

Heavy quark potential at finite temperature from gauge-string duality

A static string in an AdS Schwarzschild space is dual to a heavy quark-antiquark pair in a gauge theory at high temperature. This space is nonconfining in the sense that the energy is finite for infinite quark-antiquark separation. We introduce an infrared cutoff in this space and calculate the corresponding string energy. We find a deconfining phase transition at a critical temperature ${T}_{C}$. Above ${T}_{C}$, the string tension vanishes representing the deconfined phase. Below ${T}_{C}$, we find a linear confining behavior for large quark-antiquark separation. This simple phenomenological model leads to the appropriate zero temperature limit, corresponding to the Cornell potential and also describes a thermal deconfining phase transition. However, the temperature corrections to the string tension do not recover the expected results for low temperatures.

Generalized Friedmann equations for a finite thick brane

We present the generalized Friedmann equations describing the cosmological evolution of a finite thick brane immeresed in a five-dimensional Schwarzschild Anti-de Sitter spacetime. A linear term in the density in addition to a quatratic one arises in the Friedmann equation, leading to the standard cosmological evolution at late times without introducing an ad hoc tension term for the brane. The effective four-dimensional cosmological constant is then uplifted similar to the KKLT effect and vanishes for a brane thickness equal to the AdS curvature size, up to the third order of the thickness. The four-dimensional gravitational constant is then equal to the five-dimensional one divided by the AdS curvature radius, similar to that derived by dimensional compactification. An accelerating brane cosmology may emerge at late times provided there is either a negative transverse pressure component in the brane energy-momentum tensor or the effective brane cosmological constant is positive.

Energy distribution in Reissner–Nordström anti-de Sitter black holes in the Møller prescription

The energy (due to matter plus fields including gravity) distribution of the Reissner–Nordstrom anti-de Sitter (RN AdS) black holes is studied by using the Moller energy-momentum definition in general relativity. This result is compared with the energy expression obtained by using the Einstein and Tolman complexes. The total energy depends on the black hole mass M and charge Q and the cosmological constant Λ. The energy distribution of the RN AdS is also calculated by using the Moller prescription in teleparallel gravity. We get the same result for both of these different gravitation theories. The energy obtained is also independent of the teleparallel dimensionless coupling constant, which means that it is valid not only in the teleparallel equivalent of general relativity, but also in any teleparallel model. In special cases of our model, we also discuss the energy distributions associated with the Schwarzschild AdS, RN and Schwarzschild black holes, respectively.

Quasinormal modes of plane-symmetric anti-de Sitter black holes: A complete analysis of the gravitational perturbations

We study in detail the quasinormal modes of linear gravitational perturbations of plane-symmetric anti-de Sitter black holes. The wave equations are obtained by means of the Newman-Penrose formalism and the Chandrasekhar transformation theory. We show that oscillatory modes decay exponentially with time such that these black holes are stable against gravitational perturbations. Our numerical results show that in the large (small) black hole regime the frequencies of the ordinary quasinormal modes are proportional to the horizon radius ${r}_{+}$ (wave number $k$). The frequency of the purely damped mode is very close to the algebraically special frequency in the small horizon limit, and goes as $i{k}^{2}/3{r}_{+}$ in the opposite limit. This result is confirmed by an analytical method based on the power series expansion of the frequency in terms of the horizon radius. The same procedure applied to the Schwarzschild anti-de Sitter spacetime proves that the purely damped frequency goes as $i(l\ensuremath{-}1)(l+2)/3{r}_{+}$, where $l$ is the quantum number characterizing the angular distribution. Finally, we study the limit of high overtones and find that the frequencies become evenly spaced in this regime. The spacing of the frequency per unit horizon radius seems to be a universal quantity, in the sense that it is independent of the wave number, perturbation parity, and black hole size.

A WKB approach to scalar fields dynamics in curved space–time

Quantum fields exhibit non-trivial behaviours in curved space–times, especially around black holes or when a cosmological constant is added to the field equations. A new scheme, based on the Wentzel–Kramers–Brillouin (WKB) approximation is presented. The main advantage of this method is to allow for a better physical understanding of previously known results and to give good orders of magnitude in situations where no other approaches are currently developed. Greybody factors for evaporating black holes are rederived in this framework and the energy levels of scalar fields in the anti-de Sitter (AdS) space–time are accurately obtained. Stationary solutions in the Schwarzschild–anti-de Sitter (SAdS) background are investigated. Some improvements and the basics of a line of thought for more complex situations are suggested.

THE GENERALIZED UNCERTAINTY PRINCIPLE AND CORRECTIONS TO THE CARDY–VERLINDE FORMULA IN SAdS5 BLACK HOLES

In this paper, we investigate a possible modification to the temperature and entropy of five-dimensional Schwarzschild anti-de Sitter black holes due to the incorporation of stringy corrections to the modified uncertainty principle. Then, we subsequently argue for corrections to the Cardy–Verlinde formula in order to account for the corrected entropy. Then, we show that one can taking into account the generalized uncertainty principle corrections of the Cardy–Verlinde entropy formula by just redefining the Virasoro operator L0 and the central charge c.

Bouncing cosmology in three dimensions

We consider a dynamical two-brane in a four-dimensional black hole background withscalar hair. At high temperature this black hole goes through a phase transition byradiating away the scalar. The end phase is a topological anti-de Sitter–Schwarzschild blackhole. We argue here that for a sufficiently low temperature, the brane motionin this geometry is non-singular. This results in a universe which passes overfrom a contracting phase to an expanding one without reaching a singularity.

No Hawking–Page phase transition in three dimensions

We investigate whether or not the Hawking–Page phase transition is possible to occur in three dimensions. Starting with the simplest class of Lanczos–Lovelock action, thermodynamic behavior of all AdS-type black holes without charge falls into two classes: Schwarzschild–AdS black holes in even dimensions and Chern–Simons black holes in odd dimensions. The former class can provide the Hawking–Page transition between Schwarzschild–AdS black holes and thermal AdS space. On the other hand, the latter class is exceptional and thus the Hawking–Page transition is hard to occur. In three dimensions, a second-order phase transition might occur between the non-rotating BTZ black hole and the massless BTZ black hole (thermal AdS space), instead of the first-order Hawking–Page transition between the non-rotating BTZ black hole and thermal AdS space.

Braneworld resonances

We investigate in detail gravitational waves in an Schwarzschild–anti-de Sitter bulk spacetime surrounded by an Einstein-static brane with generic matter content. Such a model provides a useful analogy to braneworld cosmology at various stages of its evolution and generalizes our previous work (Seahra et al 2005 Class. Quantum Grav. 22 L91–101) on pure tension Einstein-static branes. We find that the behaviour of tensor-mode perturbations is completely dominated by quasi-normal modes, and we use a variety of numeric and analytic techniques to find the frequencies and lifetimes of these excitations. The parameter space governing the model yields a rich variety of resonant phenomena, which we thoroughly explore. We find that certain configurations can support a number of lightly damped ‘quasi-bound states’. A zero-mode which reproduces four-dimensional general relativity is recovered on infinitely large branes. We also examine the problem in the time domain using Green's function techniques in addition to direct numeric integration. We conclude by discussing how the quasi-normal resonances we find here can impact on braneworld cosmology.

Warped products and the Reissner–Nordström–AdS black hole

We study a multiply warped product manifold associated with the Reissner–Nordstrom–AdS metric to investigate the physical properties inside the black hole event horizons. Our results include various limiting geometries of the RN, Schwarzschild–AdS and Schwarzschild spacetimes, through the successive truncation procedure of parameters in the original curved space.

The self-gravitational corrections as the source for stiff matter on the brane in [formula omitted] bulk

A D3-brane with non-zero energy density is considered as the boundary of a five-dimensional Schwarzschild–anti-de Sitter bulk background. Taking into account the semi-classical corrections to the black hole entropy that arise as a result of the self-gravitational effect, and employing the AdS/CFT correspondence, we obtain the self-gravitational correction to the first Friedmann-like equation. The additional term in the Hubble equation due to the self-gravitational effect goes as a−6. Thus, the self-gravitational corrections act as a source of stiff matter contrary to standard FRW cosmology where the charge of the black hole plays this role.

An absence theorem for static wave maps in the Schwarzschild–AdS spacetime

In this Letter, we obtain an absence theorem for static wave maps defined from the Schwarzschild–anti de Sitter spacetime into any Riemannian manifold. This work extends the results in [Chinese Ann. Math. B 5 (1984) 737, Lett. Math. Phys. 14 (1987) 343].

CIRCULAR ORBITS AROUND SCHWARZSCHILD–AdS SPACETIME

In this paper we discuss parallel transport of vectors and spinors around circular orbits in Schwarzschild–AdS spacetime. We study the global properties of this spacetime via loop variables or holonomy. A set of paths in this background is considered. We demonstrate that for some special radii there appears the so-called quantized band structure of holonomy invariance. This analysis is also extended to parallel transport of a spinor in this spacetime.

Asymptotic quasinormal frequencies for black holes in nonasymptotically flat space–times

The exact computation of asymptotic quasinormal frequencies is a technical problem which involves the analytic continuation of a Schrödinger-type equation to the complex plane and then performing a method of monodromy matching at several poles in the plane. While this method was successfully used in asymptotically flat space–time, as applied to both the Schwarzschild and Reissner–Nordstro/m solutions, its extension to nonasymptotically flat space–times has not been achieved yet. In this work it is shown how to extend the method to this case, with the explicit analysis of Schwarzschild–de Sitter and large Schwarzschild–anti–de Sitter black holes, both in four dimensions. We obtain, for the first time, analytic expressions for the asymptotic quasinormal frequencies of these black hole space–times, and our results match previous numerical calculations with great accuracy. We also list some results concerning the general classification of asymptotic quasinormal frequencies in d-dimensional space–times.

Back Reaction in Static Einstein Spaces—Change of Entropy

Using the thermodynamical approach and the method of York, the back-reaction of anti-de Sitter Schwarzschild black hole in thermal equilibrium with conformal spin-2 field is studied. It is found that both approaches give identical results.