Holes In Anti-de Sitter Spacetime Research Articles

Heat engines for dilatonic Born\u2013Infeld black holes

In the context of dilaton coupled Einstein gravity with a negative cosmological constant and a Born–Infeld field, we study heat engines where a charged black hole is the working substance. Using the existence of a notion of thermodynamic mass and volume (which depend on the dilaton coupling), the mechanical work takes place via the pdV terms present in the first law of extended gravitational thermodynamics. The efficiency is analyzed as a function of dilaton and Born–Infeld couplings, and the results are compared with analogous computations in the related conformal solutions in the Brans–Dicke–Born–Infeld theory and black holes in anti-de Sitter space-time.

Critical phenomena of regular black holes in anti-de Sitter space-time

In General Relativity, addressing coupling to a non-linear electromagnetic field, together with a negative cosmological constant, we obtain the general static spherical symmetric black hole solution with magnetic charges, which is asymptotic to anti-de Sitter (AdS) space-times. In particular, for a degenerate case the solution becomes a Hayward–AdS black hole, which is regular everywhere in the full space-time. The existence of such a regular black hole solution preserves the weak energy condition, while the strong energy condition is violated. We then derive the first law and the Smarr formula of the black hole solution. We further discuss its thermodynamic properties and study the critical phenomena in the extended phase space where the cosmological constant is treated as a thermodynamic variable as well as the parameter associated with the non-linear electrodynamics. We obtain many interesting results such as: the Maxwell equal area law in the P{-}V (or S{-}T) diagram is violated and consequently the critical point (T_*,P_*) of the first order small–large black hole transition does not coincide with the inflection point (T_c,P_c) of the isotherms; the Clapeyron equation describing the coexistence curve of the Van der Waals (vdW) fluid is no longer valid; the heat capacity at constant pressure is finite at the critical point; the various exponents near the critical point are also different from those of the vdW fluid.

P–v criticality in the extended phase space of a noncommutative geometry inspired Reissner–Nordström black hole in AdS space-time

The P–v criticality and phase transition in the extended phase space of a noncommutative geometry inspired Reissner–Nordstrom (RN) black hole in Anti-de Sitter (AdS) space-time are studied, where the cosmological constant appears as a dynamical pressure and its conjugate quantity is thermodynamic volume of the black hole. It is found that the P–v criticality and the small black hole/large black hole phase transition appear for the noncommutative RN-AdS black hole. Numerical calculations indicate that the noncommutative parameter affects the phase transition as well as the critical temperature, horizon radius, pressure and ratio. The critical ratio is no longer universal, which is different from the result in the van de Waals liquid–gas system. The nature of phase transition at the critical point is also discussed. Especially, for the noncommutative geometry inspired RN-AdS black hole, a new thermodynamic quantity $$\varPsi $$ conjugate to the noncommutative parameter $$\theta $$ has to be defined further, which is required for consistency of both the first law of thermodynamics and the corresponding Smarr relation.

P-V criticality in the extended phase space of charged f(R) black holes in AdS space-time

The criticality and phase transition in the extended phase space of charged f(R) black holes in Anti-de Sitter (AdS) space-time are studied, where the cosmological constant appears as a dynamical pressure and its conjugate quantity is a thermodynamic volume of the black holes. We take into account three-dimensional and higher-dimensional black holes of the f(R) theory coupled to a conformally invariant Maxwell (CIM) field and find that for a f(R) black hole in three-dimensional space-time, critical behavior cannot occur; for a f(R) black hole in higher-dimensional space-time, no criticality occurs in n = 8 dimensions either, while criticality and the small-black-hole/large-black-hole phase transition appears in n = 12 dimensions. It is shown that the f(R) correction affects the phase transition as well as the critical temperature, volume and pressure. In addition, we also discuss the critical exponents at the critical point for the f(R) black hole in n space-time dimensions and show that they are the same as those in the van de Waals liquid-gas system.

Hawking evaporation time scale of topological black holes in anti-de Sitter spacetime

It was recently pointed out that if an absorbing boundary condition is imposed at infinity, an asymptotically anti-de Sitter Schwarzschild black hole with a spherical horizon takes only a finite amount of time to evaporate away even if its initial mass is arbitrarily large. We show that this is a rather generic property in AdS spacetimes: regardless of their horizon topologies, neutral AdS black holes in general relativity take about the same amount of time to evaporate down to the same size of order L, the AdS length scale. Our discussion focuses on the case in which the black hole has toral event horizon. A brief comment is made on the hyperbolic case, i.e. for black holes with negatively curved horizons.

Stability of Gauss-Bonnet black holes in anti-de Sitter space-time against scalar field condensation

We study the stability of static, hyperbolic Gauss-Bonnet black holes in ($4+1$)-dimensional anti-de Sitter (AdS) space-time against the formation of scalar hair. Close to extremality the black holes possess a near-horizon topology of ${\mathrm{AdS}}_{2}\ifmmode\times\else\texttimes\fi{}{H}^{3}$ such that within a certain range of the scalar field mass one would expect that they become unstable to the condensation of an uncharged scalar field. We confirm this numerically and observe that there exists a family of hairy black hole solutions labeled by the number of nodes of the scalar field function. We construct explicit examples of solutions with a scalar field that possesses zero nodes, one node, and two nodes, respectively, and show that the solutions with nodes persist in the limit of Einstein gravity, i.e. for vanishing Gauss-Bonnet coupling. We observe that the interval of the mass for which scalar field condensation appears decreases with increasing Gauss-Bonnet coupling and/or with increasing node number.

Thermodynamics of DBI Black Holes in Anti-de Sitter Spacetime

Through the gauge field theory, we obtain the solution of the DBI-AdS black hole. In the meantime, according to the relations between the action and the grand partition function, we obtain the grand partition function in the DBI-AdS black hole. The temperature and the potential of the DBI-AdS black hole are gained from differential of the grand partition function. With the thermodynamic relations, other thermodynamics are also obtained. The solution and the thermodynamics of the DBI-AdS black hole are turned out that they can reduce to the case of a charged black hole in four-dimensional spacetimes.

Black holes in modified gravity theories

In the context of f(R) gravity theories, the issue of finding static and spherically symmetric black hole solutions is addressed. Two approaches to study the existence of such solutions are considered: first, constant curvature solutions, and second, the general case (without imposing constant curvature) is also studied. Performing a perturbative expansion around the Einstein-Hilbert action, it is found that only solutions of the Schwarzschild-(Anti-) de Sitter type are present (up to second order in perturbations) and the explicit expressions for these solutions are provided in terms of the f(R) function. Finally we consider the thermodynamics of black holes in Anti-de Sitter space-time and study their local and global stability.

Black holes inf(R)theories

In the context of $f(R)$ theories of gravity, we address the problem of finding static and spherically symmetric black hole solutions. Several aspects of constant curvature solutions with and without electric charge are discussed. We also study the general case (without imposing constant curvature). Following a perturbative approach around the Einstein-Hilbert action, it is found that only solutions of the Schwarzschild-(anti) de Sitter type are present up to second order in perturbations. Explicit expressions for the effective cosmological constant are obtained in terms of the $f(R)$ function. Finally, we have considered the thermodynamics of black holes in anti-de Sitter space-time and found that this kind of solutions can only exist provided the theory satisfies $R_0+f(R_0)<0$. Interestingly, this expression is related to the condition which guarantees the positivity of the effective Newton's constant in this type of theories. In addition, it also ensures that the thermodynamical properties in $f(R)$ gravities are qualitatively similar to those of standard General Relativity.

Dyonic AdS black holes from magnetohydrodynamics

We use the AdS/CFT correspondence to argue that large dyonic black holes in anti-de Sitter spacetime are dual to stationary solutions of the equations of relativistic magnetohydrodynamics on the conformal boundary of AdS. The dyonic Kerr-Newman-AdS4 solution corresponds to a charged diamagnetic fluid not subject to any net Lorentz force, due to orthogonal magnetic and electric fields compensating each other. The conserved charges, stress tensor and R-current of the fluid are shown to be in exact agreement with the corresponding quantities of the black hole. Furthermore, we obtain stationary solutions of the Navier-Stokes equations in four dimensions, which yield predictions for (yet to be constructed) charged rotating black strings in AdS5 carrying nonvanishing momentum along the string. Finally, we consider Scherk-Schwarz reduced AdS gravity on a circle. In this theory, large black holes and black strings are dual to lumps of deconfined plasma of the associated CFT. We analyze the effects that a magnetic field introduces in the Rayleigh-Plateau instability of a plasma tube, which is holographically dual to the Gregory-Laflamme instability of a magnetically charged black string.

Hawking Radiation of Charged Particles via Tunneling from aCylindrically Symmetric Black Hole in Anti-de Sitter Space-Time

Applying Parikh–Wilzcek's semi-classical quantumtunneling model, we study the Hawking radiation of charged particles astunneling from the event horizon of a cylindrically symmetric black hole inanti-de Sitter space-time. The derived result shows that the tunneling rateof charged particles is related to the change ofBekenstein–Hawking entropy and that the radiation spectrum is notstrictly pure thermal after taking the black hole background dynamicaland self-gravitation interaction into account, but is consistentwith the underlying unitary theory.

Kaluza-Klein black hole with negatively curved extra dimensions in string-generated gravity models

We obtain a new exact black-hole solution in Einstein-Gauss-Bonnet gravity with a cosmological constant which bears a specific relation to the Gauss-Bonnet coupling constant. The spacetime is a product of the usual 4-dimensional manifold with a $(n-4)$-dimensional space of constant negative curvature, i.e., its topology is locally ${\ma M}^n \approx {\ma M}^4 \times {\ma H}^{n-4}$. The solution has two parameters and asymptotically approximates to the field of a charged black hole in anti-de Sitter spacetime. The most interesting and remarkable feature is that the Gauss-Bonnet term acts like a Maxwell source for large $r$ while at the other end it regularizes the metric and weakens the central singularity.

Quantum entropy of cylindrical black hole in Anti-de Sitter space-time

By using the brick-wall model, the quantum entropy of a cylindrical black hole in Anti-de Sitter space-time arising from the massless Dirac field is discussed. It is shown that the quantum entropy has both linear and logarithmical divergences if the usual contribution from the vacuum surrounding the system is ignored, and the whole expression does not take the form of the scalar one. Both the whole logarithmic term and the subleading logarithmic term which relates to the spins of the Dirac particles are always positive.

Orbifold physics and de Sitter spacetime

It is generally believed the way to resolve the black hole information paradox in string theory is to embed the black hole in anti-de Sitter 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 which are compatible with local de Sitter geometry, while still allowing the simplest versions.

Divergence structure for the quantum entropy of black holes in Anti-de Sitter spacetime

Divergence structure for the quantum entropy of a black hole in Anti-de Sitter spacetime due to the electromagnetic and gravitational fields is investigated by using the brick-wall model. The entropy has both linearly and logarithmically divergent terms, where the linearly divergent term can reduce to the form proportional to the event horizon area if the temperature is replaced by the Hawking temperature and the coordinate cutoff is replaced by the proper cutoff; while the logarithmic divergences not only depend on the characteristics of the black hole but also on the spin of the fields. Since this term exists, the contribution of a spin field in general is not proportional to the scalar one.

The Fefferman-Graham ambiguity and AdS black holes

Asymptotically anti-de Sitter space-times in pure gravity with negative cosmological constant are described, in all space-time dimensions greater than two, by classical degrees of freedom on the conformal boundary at space-like infinity. Their effective boundary action has a conformal anomaly for even dimensions and is conformally invariant for odd ones. These degrees of freedom are encoded in traceless tensor fields in the Fefferman-Graham asymptotic metric for any choice of conformally flat boundary and generate all Schwarzschild and Kerr black holes in anti-de Sitter space-time. We argue that these fields describe components of an energy-momentum tensor of a boundary theory and show explicitly how this is realized in 2+1 dimensions. There, the Fefferman-Graham fields reduce to the generators of the Virasoro algebra and give the mass and the angular momentum of the BTZ black holes. Their local expression is the Liouville field in a general curved background.

Comments on black holes in string theory

A very brief review is given of some of the developments leading to our current understanding of black holes in string theory. This is followed by a discussion of two possible misconceptions in this subject - one involving the stability of small black holes and the other involving scale radius duality. Finally, I describe some recent results concerning quasinormal modes of black holes in anti-de Sitter spacetime, and their implications for strongly coupled conformal field theories (in various dimensions).

Charged AdS black holes and catastrophic holography

We compute the properties of a class of charged black holes in anti-de Sitter space-time, in diverse dimensions. These black holes are solutions of consistent Einstein-Maxwell truncations of gauged supergravities, which are shown to arise from the inclusion of rotation in the transverse space. We uncover rich thermodynamic phase structures for these systems, which display classic critical phenomena, including structures isomorphic to the van der Waals-Maxwell liquid-gas system. In that case, the phases are controlled by the universal `cusp' and `swallowtail' shapes familiar from catastrophe theory. All of the thermodynamics is consistent with field theory interpretations via holography, where the dual field theories can sometimes be found on the world volumes of coincident rotating branes.

Thermodynamics of charged anti-de Sitter black holes in canonical ensemble

As in the grand canonical treatment of Reissner–Nordström black holes in anti-de Sitter spacetime, the canonical ensemble formulation also shows that non-extremal black holes tend to have lower action than extremal ones. However, some small non-extremal black holes have higher action, leading to the possibility of transitions between non-extremal and extremal black holes.

Geometrical properties of Gauge theories: M. Grabiak, W. Greiner, and B. Müller. Institut für theoretische physik der Johann Wolfgang Goethe-Universität, Robert-Mayer-Straße 8-10, Postfach 111932, D-6000 Frankfurt am Main 11, West Germany

Asymptotically anti-de Sitter space-times in pure gravity with negative cosmological constant are described, in all space-time dimensions greater than two, by classical degrees of freedom on the conformal boundary at space-like infinity. Their effective boundary action has a conformal anomaly for even dimensions and is conformally invariant for odd ones. These degrees of freedom are encoded in traceless tensor fields in the Fefferman-Graham asymptotic metric for any choice of conformally flat boundary and generate all Schwarzschild and Kerr black holes in anti-de Sitter space-time. We argue that these fields describe components of an energy-momentum tensor of a boundary theory and show explicitly how this is realized in 2+1 dimensions. There, the Fefferman-Graham fields reduce to the generators of the Virasoro algebra and give the mass and the angular momentum of the BTZ black holes. Their local expression is the Liouville field in a general curved background.