Toroidal Black Holes Research Articles

The special role of toroidal black holes in holography

In the standard holographic ``dictionary'', the deep infrared of the strongly coupled boundary field theory is studied by examining the bulk region near to the event horizon of a simple AdS-Reissner-Nordstr\"{o}m black hole, near to extremality. Recently Horowitz et al. have argued that this is not correct, \emph{except} in the case of small toroidal black holes, which are therefore revealed to be particularly interesting and important. On the other hand, the Weak Gravity Conjecture postulates that black holes (including toroidal black holes) which are extremely near to extremality spontaneously emit black holes of the same kind. We show that, in the toroidal case, these ``emitted'' black holes are always small in the sense of Horowitz et al. As an application, we discuss the Grinberg-Maldacena analysis of the way one-point functions, evaluated outside an AdS-Reissner-Nordstr\"{o}m black hole, depend on the proper time of fall from the event horizon to the Cauchy horizon. We find that, for emitted toroidal black holes, this dependence effectively drops out.

Topological black holes in higher derivative gravity

We study static black holes in quadratic gravity with planar and hyperbolic symmetry and non-extremal horizons. We obtain a solution in terms of an infinite power-series expansion around the horizon, which is characterized by two independent integration constants – the black hole radius and the strength of the Bach tensor at the horizon. While in Einstein’s gravity, such black holes require a negative cosmological constant Lambda , in quadratic gravity they can exist for any sign of Lambda and also for Lambda =0. Different branches of Schwarzschild–Bach–(A)dS or purely Bachian black holes are identified which admit distinct Einstein limits. Depending on the curvature of the transverse space and the value of Lambda , these Einstein limits result in (A)dS–Schwarzschild spacetimes with a transverse space of arbitrary curvature (such as black holes and naked singularities) or in Kundt metrics of the (anti-)Nariai type (i.e., dS_2times S^2, AdS_2times H^2, and flat spacetime). In the special case of toroidal black holes with Lambda =0, we also discuss how the Bach parameter needs to be fine-tuned to ensure that the metric does not blow up near infinity and instead matches asymptotically a Ricci-flat solution.

How anti-de Sitter black holes reach thermal equilibrium

It is commonly known in the literature that large black holes in anti-de Sitter spacetimes (with reflective boundary condition) are in thermal equilibrium with their Hawking radiation. Focusing on black holes with event horizon of toroidal topology, we study a simple model to understand explicitly how this thermal equilibrium is reached under Hawking evaporation. It is shown that it is possible for a large toroidal black hole to evolve into a small (but stable) one.

Thermodynamic functions of toroidal black holes

The thermodynamic functions of toroidal black holes are investigated in this paper by taking the cosmological constant as a dynamic variable equivalent to the pressure. The equation of state and the Smarr relation of a toroidal black hole are given. Then, the Gibbs function is obtained by calculating the Euclidian action. Further we study other thermodynamic functions of the toroidal black hole, such as, the free energy, internal energy and thermodynamic enthalpy. The heat capacities of the toroidal black hole at constant pressure and constant volume are obtained as well. The results show that toroidal black holes have no van der Waals type phase transition. Toroidal black hole is a stable thermodynamic system because its constant pressure heat capacity is greater than zero and constant volume heat capacity is equal to zero.

Thermodynamic functions of toroidal black holes

The thermodynamic functions of toroidal black holes are investigated in this paper by taking the cosmological constant as a dynamic variable equivalent to the pressure. The equation of state and the Smarr relation of a toroidal black hole are given. Then, the Gibbs function is obtained by calculating the Euclidian action. Further we study other thermodynamic functions of the toroidal black hole, such as free energy, internal energy, and thermodynamic enthalpy. The heat capacity of the toroidal black hole at constant pressure and constant volume is obtained. The results show that toroidal black holes have no van der Waals type phase transition. Toroidal black hole is a stable thermodynamic system because its heat capacity at constant pressure is greater than zero and its heat capacity at constant volume is equal to zero.

New class of solutions in f(R)-gravity's rainbow and f(R)-gravity: Exact solutions+thermodynamics+quasinormal modes

This paper is devoted to the obtaining of the exact solutions in the framework of modified f(R)-gravity's rainbow(UV completion of General Relativity)/f(R)-gravity and the study of their thermodynamic behavior. In the f(R)-gravity's rainbow, we have analyzed the concept of effective potential barrier by transforming the radial equation of motion into standard Schrodinger form (we should note that scalar field Ψ(x) couples to gravity minimally or non-minimally with coupling constant λ and the gravity representation which is coupled with the scalar field is f(R) not just R). The most important result derived from this study is that gravity's rainbow increases the height of this potential in the exterior region of the event horizon. We also figure out the effect of the coupling constant λ and the f(R) parameter η on the height of the potential barrier and the other thermodynamical quantities like temperature and heat capacity. We have shown that the effect of f(R)-gravity on the temperature adds a coefficient of 1/2 to the cosmological constant.1 We study the quasinormal modes (QNMs) of 3D black holes in the f(R)-gravity's rainbow. For this purpose, we use the WKB approximation method upto third order corrections. We have shown the perturbations decay in corresponding diagrams when the coupling constant λ and rainbow function g(ε) change. We also obtain two different solutions when Ricci scalar is constant. The first one is for a charged slowly rotating toroidal black holes and the second one is for a higher dimensional toroidal black holes inspired by non-commutative geometry. The source for the second one is given by a fluid-type matter with the Gaussian-distribution smeared mass density. In Starobinsky model we show that the charged slowly rotating solution is ill-defined for s2=1 value.

Charged slowly rotating toroidal black holes in the (1 + 3)-dimensional Einstein-power-Maxwell theory

In this work, we find charged slowly rotating solutions in the four-dimensional Einstein-power-Maxwell nonlinear electrodynamics assuming a negative cosmological constant. By solving the system of coupled field equations explicitly, we obtain an approximate analytical solution in the small rotation limit. The solution obtained is characterized by a flat horizon structure, and it corresponds to a toroidal black hole. The Smarr’s formula, the thermodynamics and the invariants Ricci scalar and Kretschmann scalar are briefly discussed.

Throat quantization of the Schwarzschild-Tangherlini(-AdS) black hole

By the throat quantization pioneered by Louko and Mäkelä, we derive the mass and area/entropy spectra for the Schwarzschild-Tangherlini-type asymptotically flat or AdS vacuum black hole in arbitrary dimensions. Using the WKB approximation for black holes with large mass, we show that area/entropy is equally spaced for asymptotically flat black holes, while mass is equally spaced for asymptotically AdS black holes. Exact spectra can be obtained for toroidal AdS black holes in arbitrary dimensions including the three-dimensional BTZ black hole.

Exact time-dependent states for throat quantized toroidal AdS black holes

We investigate exact non-stationary quantum states of vacuum toroidal black holes with a negative cosmological constant in arbitrary dimensions using the framework of throat quantization pioneered by Louko and M\"akel\"a for Schwarzschild black holes. The system is equivalent to a harmonic oscillator on the half line, in which the central singularity is resolved quantum mechanically by imposing suitable boundary conditions that preserve unitarity. We identify two suitable families of exact time-dependent wave functions with Dirichlet or Neumann boundary conditions at the location of the classical singularity. We find that for highly non-stationary states of large-mass black holes, quantum fluctuations are not negligible in one family, while they are greatly suppressed in the other. The latter, therefore, may provide candidates for describing the dynamics of semi-classical black holes.

Bounds on the local energy density of holographic CFTs from bulk geometry

The stress tensor is a basic local operator in any field theory; in the context of AdS/CFT, it is the operator which is dual to the bulk geometry itself. Here we exploit this feature by using the bulk geometry to place constraints on the local energy density in static states of holographic (2+1)-dimensional CFTs living on a closed (but otherwise generally curved) spatial geometry. We allow for the presence of a marginal scalar deformation, dual to a massless scalar field in the bulk. For certain vacuum states in which the bulk geometry is well-behaved at zero temperature, we find that the bulk equations of motion imply that the local energy density integrated over specific boundary domains is negative. In the absence of scalar deformations, we use the inverse mean curvature flow to show that if the CFT spatial geometry has spherical topology but non-constant curvature, the local energy density must be positive somewhere. This result extends to other topologies, but only for certain types of vacuum; in particular, for a generic toroidal boundary, the vacuum’s bulk dual must be the zero-temperature limit of a toroidal black hole.

Throat quantization of the Schwarzschild–Tangherlini(-AdS) black hole

Adopting the throat quantization pioneered by Louko and Mäkelä, we derive the mass and area spectra for the Schwarzschild–Tangherlini black hole and its anti-de Sitter (AdS) generalization in arbitrary dimensions. We find that the system can be quantized exactly in three special cases: the three-dimensional BTZ black hole, toroidal black holes in any dimension, and five-dimensional Schwarzshild–Tangherlini(-AdS) black holes. For the remaining cases the spectra are obtained for large mass using the WKB approximation. For asymptotically flat black holes, the area/entropy has an equally spaced spectrum, as expected from previous work. In the asymptotically AdS case on the other hand, it is the mass spectrum that is equally spaced. Our exact results for the BTZ black hole mass with Dirichlet boundary conditions are consistent with the spectra of the corresponding operators in the dual CFT.

Black branes in AdS: BPS bounds and asymptotic charges

AbstractWe focus on black branes and toroidal black holes in N = 2 gauged supergravities that asymptote to AdS4, and derive formulas for the mass and central charge densities. We derive the corresponding BPS bound from the superalgebra of the asymptotic vacuum and illustrate our procedure with explicit examples of genuine black brane solutions with non‐trivial scalars.

Thermodynamic geometry and critical behavior of a toroidal black hole

In this paper,we study the thermodynamic properties of a toroidal black hole from a geometric viewpoint.After the temperature and heat capacity of the black hole have been calculated,we investigate the relationship between its thermodynamic geometry metric and critical behavior,as well as phase transition characteristics.The results show that the temperature of the toroidal black hole is equal to its Hawking temperature.Moreover,because its curvature scalar is zero,the Weinhold geometry fails to provide some information about the critical behavior and phase transition characteristics of the toroidal black hole.But the Ruppeiner geometry and the Legendre invariant metric can provide a good description of its phase structure.

De Broglie–Bohm interpretation for wave function of a toroidal black hole

The mass function of a toroidal black hole as a dynamical variable is given by using Kuchar’s approach. Then the toroidal black hole is investigated by using the de Broglie–Bohm approach, and its quantum potential and quantum trajectories are obtained. In our process the vector potential of the electromagnetic field in the toroidal black hole is treated as a canonical variable.

Entropy of quantum field in toroidal black hole without brick wall

In this paper the entropy of a toroidal black hole due to a scalar field is investigated by using the DLM scheme. The entropy is renormalized to the standard Bekenstein-Hawking formula with a one-loop correction arising from the higher curvature terms of the gravitational action. For the scalar field, the renormalized Newton constant and two renormalized coupling constants in the toroidal black hole are the same as those in the Reissner-Nordstrom black hole except for other one.

Entropy of toroidal black hole to all orders in the Planck length

Entropy of toroidal black hole to all orders in the Planck length

TUNNELING RADIATION FROM TOROIDAL BLACK HOLE

The tunneling radiation from toroidal black hole is studied by applying the method of Parikh. The appearance of higher corrections to the semiclassical rate caused by the law of energy conservation is demonstrated and it is shown that the energy spectrum deviates from exact thermal spectrum.

Quantum entropy of Dirac field in toroidal black hole

The quantum entropy of Dirac field in toroidal black hole is considered and the effects of the spins of the Dirac particles on the entropy are investigated using brick-wall model. It is shown that the quantum entropy has both linearly and logarithmically divergent terms and it has the different structure from that of the black hole. It is also shown that the contribution of the subleading logarithmic term which relates to the spins of the Dirac particles are always positive.

UNCERTAINTY RELATION AND BLACK HOLE ENTROPY OF TOROIDAL SPACETIME

By using the method of quantum statistics and via the new equation of state density motivated by the generalized uncertainty relation in the quantum gravity, we avoid the difficulty of solving wave equation, and directly derive the partition functions of bosonic and fermionic field in Toroidal black hole. Then we calculate the entropies of bosonic and fermionic field near the black hole horizon on the background of a black hole. In our result, the divergent logarithmic term and ultraviolet cutoff in the original brick-wall method by which the black hole entropy was derived no longer exist. It is shown that the entropy of the black hole is proportional to the area of the horizon. These results are similar to that in the black hole with horizon topology S2.

Entropies of a Toroidal Black Hole Due to Scalar and Dirac Fields

Using the thin film brick-wall model, the entropies of a toroidal black hole due to scalar and Dirac fields are investigated. The entropy due to the scalar field is one fourth of the horizon area, and that due to the Dirac field is seven eighth of the area. These results are similar to that in black holes with horizon topology S2. The cutoff in toroidal black hole is chosen as the same as one in black holes with horizon topology S2, which seems to mean that the thin film brick-wall model is universal.