Topological Black Holes Research Articles

QUASINORMAL MODES AND STABILITY ANALYSIS FOR Z = 4 TOPOLOGICAL BLACK HOLE IN 4 + 1-DIMENSIONAL HORAVA–LIFSHITZ GRAVITY

We study the stability of z = 4 topological black hole in 4 + 1-dimensional Horava–Lifshitz gravity against scalar perturbations by analyzing the quasinormal modes (QNMs). It is possible to distinguish two cases for which the black hole is stable. The first one occurs when p + Q > 0 and QNMs are characterized by a real and imaginary part, meaning that the field has oscillatory modes but with Im (ω) < 0; therefore, it is stable. While in the second case p + Q < 0, QNMs are purely imaginary ( Im (ω) < 0) and then absolutely damped.

Quasinormal modes, stability analysis and absorption cross section for 4-dimensional topological Lifshitz black hole

We study scalar perturbations in the background of a Topological Lifshitz black hole in four dimensions. We compute analytically the quasinormal modes and from these modes we show that Topological Lifshitz black hole is stable. On the other hand, we compute the reflection and transmission coefficients and the absorption cross section and we show that there is a range of modes with high angular momentum which contributes to the absorption cross section in the low frequency limit. Furthermore, in this limit, we show that the absorption cross section decreases if the scalar field mass increases, for a real scalar field mass.

Phase transition and scaling behavior of topological charged black holes in Hořava–Lifshitz gravity

Gravity can be thought as an emergent phenomenon and it has a nice ‘thermodynamic’ structure. In this context, it is then possible to study the thermodynamics without knowing the details of the underlying microscopic degrees of freedom. Here, based on the ordinary thermodynamics, we investigate the phase transition of the static, spherically symmetric charged black hole solution with the arbitrary scalar curvature 2k in Hořava–Lifshitz gravity at the Lifshitz point z = 3. The analysis is done using the canonical ensemble framework, i.e. the charge is kept fixed. We find (a) for both k = 0 and k = 1, there is no phase transition, (b) while k = −1 case exhibits the second-order phase transition within the physical region of the black hole. The critical point of second-order phase transition is obtained by the divergence of the heat capacity at constant charge. Near the critical point, we find the various critical exponents. It is also observed that they satisfy the usual thermodynamic scaling laws.

Topological electro-vacuum solutions in extended gravity

Spherically symmetric static topological black hole solutions associated with some extended higher order gravitational models in the presence of a Maxwell-field are derived by means of simple Lagrangian method, based on spherically symmetric reduction. Some new topological black hole solutions are presented and the validity of the First Law is investigated, and in these cases an expression for the energy is provided.

THERMODYNAMICS OF NONSPHERICAL BLACK HOLES FROM LIOUVILLE THEORY

A Liouville formalism was proposed many years ago to account for the black hole entropy. It was recently updated to connect thermodynamics of general black holes, in particular the Hawking temperature, to two-dimensional Liouville theory. This relies on the dimensional reduction to two-dimensional black hole metric. The relevant dilaton gravity model can be rewritten as a Liouville-like theory. We refine the method and give general formulas for the corresponding scalar and energy–momentum tensors in Liouville theory. This enables us to read off the black hole temperature using a relation which was found about three decades ago. Then the range of application is extended to include nonspherical black holes such as neutral and charged black rings, topological black hole and the case coupled to a scalar field. As for the entropy, following previous authors, we invoke the Lagrangian approach to central charge by Cadoni and then use the Cardy formula. The general relevant parameters are also given. This approach is more advantageous than the usual Hamiltonian approach which was used by the old Liouville formalism for black hole entropy.

Holographic cosmological backgrounds, Wilson loop (de)confinement and dilaton singularities

AbstractWe review a construction of holographic geometries dual to ℳ︁ = 4 SYM theory on a Friedmann‐Robertson‐Walker background and in the presence or absence of a gluon condensate and instanton density. We find the most general solution with arbitrary scale factor and show that it is diffeomorphic to topological black holes. We introduce a time‐dependent boundary cosmological constant λ(t) and show energy‐momentum conservation in this background. For constant λ, the deconfinement properties of the temporal Wilson loop are analysed. In most cases the Wilson loop confines throughout cosmological evolution. However, there is an exceptional case which shows a transition from deconfinement at early times to confinement at late times. We classify the presence or absence of horizons, with important implications for the Wilson loop.

Incompressible fluids of the de Sitter horizon and beyond

There are (at least) two surfaces of particular interest in eternal de Sitter space. One is the timelike hypersurface constituting the lab wall of a static patch observer and the other is the future boundary of global de Sitter space. We study both linear and non-linear deformations of four-dimensional de Sitter space which obey the Einstein equation. Our deformations leave the induced conformal metric and trace of the extrinsic curvature unchanged for a fixed hypersurface. This hypersurface is either timelike within the static patch or spacelike in the future diamond. We require the deformations to be regular at the future horizon of the static patch observer. For linearized perturbations in the future diamond, this corresponds to imposing incoming flux solely from the future horizon of a single static patch observer. When the slices are arbitrarily close to the cosmological horizon, the finite deformations are characterized by solutions to the incompressible Navier-Stokes equation for both spacelike and timelike hypersurfaces. We then study, at the level of linearized gravity, the change in the discrete dispersion relation as we push the timelike hypersurface toward the worldline of the static patch. Finally, we study the spectrum of linearized solutions as the spacelike slices are pushed to future infinity and relate our calculations to analogous ones in the context of massless topological black holes in AdS$_4$.

Thermodynamics of topological black holes in Hořava–Lifshitz gravity

We investigate the thermodynamic properties of the most general static, spherically symmetric, topological black holes of the Hořava-Lifshitz gravity. The mass of these black holes turns out to depend on the entropy and the cosmological constant that we consider as an additional thermodynamic variable. We study different thermodynamic ensembles and the corresponding heat capacities in order to show that second–order phase transitions occur at certain specific values of the horizon radius. Moreover, we study the geometric properties of the equilibrium space by using the formalism of geometrothermodynamics. We show that the phase transitions, which are characterized by divergencies of the heat capacities, are described in geometrothermodynamics by curvature singularities in the equilibrium space.

Immirzi parameter and Noether charges in first order gravity

The framework of SO(3,2) constrained BF theory applied to gravity makes it possible to generalize formulas for gravitational diffeomorphic Noether charges (mass, angular momentum, and entropy). It extends Wald's approach to the case of first order gravity with a negative cosmological constant, the Holst modification and the topological terms (Nieh-Yan, Euler, and Pontryagin).Topological invariants play essential role contributing to the boundary terms in the regularization scheme for the asymptotically AdS spacetimes, so that the differentiability of the action is automatically secured. Intriguingly, it turns out that the black hole thermodynamics does not depend on the Immirzi parameter for the AdS–Schwarzschild, AdS–Kerr, and topological black holes, whereas a nontrivial modification appears for the AdS–Taub–NUT spacetime, where it impacts not only the entropy, but also the total mass.

Geometrothermodynamics in Hořava–Lifshitz gravity

We investigate the thermodynamic geometries of the most general static, spherically symmetric, topological black holes of the Hořava–Lifshitz gravity. In particular, we show that a Legendre invariant metric derived in the context of geometrothermodynamics for the equilibrium manifold correctly reproduces the phase transition structure of these black holes. Moreover, the limiting cases in which the mass, entropy or Hawking temperature vanish are also accompanied by curvature singularities which indicate the limit of applicability of the thermodynamics and geometrothermodynamics of black holes. The Einstein limit and the case of a black hole with a flat horizon are also investigated.

WHAT IS THE TOPOLOGY OF A SCHWARZSCHILD BLACK HOLE?

We investigate the topology of Schwarzschild's black holes through the immersion of this space-time in space of higher dimension. Through the immersions of Kasner and Fronsdal we calculate the extension of the Schwarzschilds black hole.

You Cannot Press Out the Black Hole

It is shown that a ball-shaped black hole region homeomorphic with D**n cannot be pressed out, along whichever axis penetrating the black hole region, into a black ring with a doughnut-shaped black hole region homeomorphic with S**1 x D**(n-1). A more general prohibition law for the change of the topology of black holes, including a version of no-bifurcation theorems for black holes, is given.

Energy and Momentum of Higher Dimensional Black Holes

In this paper, we devote to investigate the energy-momentum problem of higher dimensional black holes in the general theory of relativity. The energy and momentum complex of Moller has been used for the calculations. Also, total energy and total momentum of some special cases for higher dimensional black holes such as Schwarzschild-like black holes, Reissner-Nordstrom-like charged black holes, AdS-like black holes, topological black holes, BTZ-like and charged BTZ-like black holes were obtained. It is invented that the momentum of black holes vanishes everywhere while the energy of black holes are not equal to zero in higher dimension. Also the results agree with Yang and Radinschi or Vagenas results in three and four dimensional black holes, respectively (Jang and Radinschi in AIP Conf. Proc. 895, 325, 2007; Vagenas in Mod. Phys. Lett. A 21, 1947, 2006).

Stability of Hořava-Lifshitz black holes in the context of AdS/CFT

The anti--de Sitter/conformal field theory (AdS/CFT) correspondence is a powerful tool that promises to provide new insights toward a full understanding of field theories under extreme conditions, including but not limited to quark-gluon plasma, Fermi liquid and superconductor. In many such applications, one typically models the field theory with asymptotically AdS black holes. These black holes are subjected to stringy effects that might render them unstable. Ho\v{r}ava-Lifshitz gravity, in which space and time undergo different transformations, has attracted attentions due to its power-counting renormalizability. In terms of AdS/CFT correspondence, Ho\v{r}ava-Lifshitz black holes might be useful to model holographic superconductors with Lifshitz scaling symmetry. It is thus interesting to study the stringy stability of Ho\v{r}ava-Lifshitz black holes in the context of AdS/CFT. We find that uncharged topological black holes in $\lambda=1$ Ho\v{r}ava-Lifshitz theory are nonperturbatively stable, unlike their counterparts in Einstein gravity, with the possible exceptions of negatively curved black holes with detailed balance parameter $\epsilon$ close to unity. Sufficiently charged flat black holes for $\epsilon$ close to unity, and sufficiently charged positively curved black holes with $\epsilon$ close to zero, are also unstable. The implication to the Ho\v{r}ava-Lifshitz holographic superconductor is discussed.

Energy issue for a class of modified higher order gravity black hole solutions

In the case of a large class of static, spherically symmetric black hole solutions in higher order modified gravity models, an expression for the associated energy is proposed and identified with a quantity proportional to the constant of integration, which appears in the explicit solution. The identification is achieved making use of derivation of the first law of black hole thermodynamics from the equations of motion, evaluating independently the entropy via the Wald method and the Hawking temperature via quantum mechanical methods in curved space-times. Several nontrivial examples are discussed, including a new topological higher derivative black hole solution, and the proposal is shown to work in all examples considered.

Towards a derivation of holographic entanglement entropy

We provide a derivation of holographic entanglement entropy for spherical entangling surfaces. Our construction relies on conformally mapping the boundary CFT to a hyperbolic geometry and observing that the vacuum state is mapped to a thermal state in the latter geometry. Hence the conformal transformation maps the entanglement entropy to the thermodynamic entropy of this thermal state. The AdS/CFT dictionary allows us to calculate this thermodynamic entropy as the horizon entropy of a certain topological black hole. In even dimensions, we also demonstrate that the universal contribution to the entanglement entropy is given by A-type trace anomaly for any CFT, without reference to holography.

Thermodynamics of Third Order Lovelock Anti-de Sitter Black Holes Revisited

We compute the mass and temperature of third order Lovelock black holes with negative Gauss—Bonnet coefficient α2 < 0 in anti-de Sitter space and perform the stability analysis of topological black holes. When k = −1, the third order Lovelock black holes are thermodynamically stable for the whole range r+. When k = 1, we found that the black hole has an intermediate unstable phase for D = 7. In eight dimensional spacetimes, however, a new phase of thermodynamically unstable small black holes appears if the coefficient is under a critical value. For D ≥ 9, black holes have similar the distributions of thermodynamically stable regions to the case where the coefficient is under a critical value for D = 8. It is worth to mention that all the thermodynamic and conserved quantities of the black holes with flat horizon do not depend on the Lovelock coefficients and are the same as those of black holes in general gravity.

THERMODYNAMICS OF GAUSS–BONNET–BORN–INFELD BLACK HOLES IN AdS SPACE

We construct solutions of a model which includes the Gauss–Bonnet and Born–Infeld terms for various horizon topologies (k = 0, ±1), and then the mass, temperature, entropy, and heat capacity of black holes are computed. For the sake of simplicity, we perform the stability analysis of five-dimensional topological black holes in AdS space.

Further Restrictions on the Topology of Stationary Black Holes in Five Dimensions

We place further restriction on the possible topology of stationary asymptotically flat vacuum black holes in five spacetime dimensions. We prove that the horizon manifold can be either a connected sum of Lens spaces and “handles” S 1 × S 2, or the quotient of S 3 by certain finite groups of isometries (with no “handles”). The resulting horizon topologies include Prism manifolds and quotients of the Poincare homology sphere. We also show that the topology of the domain of outer communication is a cartesian product of the time direction with a finite connected sum of $${\mathbb R^4,S^2 \times S^2}$$ ’s and CP 2’s, minus the black hole itself. We do not assume the existence of any Killing vector beside the asymptotically time like one required by definition for stationarity.

A Uniqueness Theorem for Stationary Kaluza-Klein Black Holes

We prove a uniqueness theorem for stationary D-dimensional Kaluza-Klein black holes with D − 2 Killing fields, generating the symmetry group $${{\mathbb R}\times U(1)^{D-3}}$$ . It is shown that the topology and metric of such black holes is uniquely determined by the angular momenta and certain other invariants consisting of a number of real moduli, as well as integer vectors subject to certain constraints.