Kerr Anti-de Sitter Black Holes Research Articles

Multicritical phase transitions in multiply rotating black holes

We show that multi-critical points in which more than three phases coalesce are present in multiply rotating Kerr-anti de Sitter black holes in d-dimensions. We explicitly present a quadruple point for a triply rotating black hole in d = 8 and a quintuple point for a quadruply rotating black hole in d = 10. The maximal number of distinct phases n is one larger than the maximal number of independent rotations, and we outline a method for obtaining the associated n-tuple point. Situations also exist where more than three phases merge at sub-maximal multi-critical points. Our results show that multi-critical points in black hole thermodynamics are more common than previously thought, with systems potentially supporting many phases as long as a sufficient number of thermodynamic variables are present.

Criticality and phase transition of Kerr–anti-de Sitter black hole with quintessence and cloud of strings

In this paper, a thermodynamical study of the Kerr–anti-de Sitter (KAdS) black hole (BH) encircled by quintessence matter and the cloud of strings is presented. We check the effects of the cloud parameter on the thermodynamical variables including Hawking temperature, entropy, Helmholtz free energy (HFE), Gibbs free energy (GFE), and specific heat capacity. These thermodynamic variables hold the Smarr–Gibbs–Dehum (SGD) relation in the appearance of quintessence and the cloud of the string parameter. Then we calculate the critical expressions of the developed variables in two different ways that are “Van-der-Waals (vdW)-type equation of state” (EoS) and the “Maxwell equal-area law” (MEAL). The latter technique is found to be more reasonable to examine the criticality of the complex BHs. Using MEAL, we plot the phase diagram in a temperature–entropy plane and obtain an isobar, which represents the co-existence region of liquid–gas phases. It is concluded that the uncharged BHs exhibit the same phase transition (PT) to vdW fluid as the temperature drops down its critical value. Also, we discuss the influence of thermal fluctuations (TF) on the stability of KAdS BH.

Correction to the tunneling radiation of arbitrary spin fermions in Kerr Anti-de Sitter black hole

According to the dispersion relation that stems from the string theory and the quantum gravitational theory, we study the dynamic equation of fermions, that is Rarita–Schwinger equation. Based on the Lorentz dispersion relation modified in the high-energy case, the dynamic equation of arbitrary spin fermions is accurately corrected in the Kerr Anti-de Sitter black hole, then the action of fermions with arbitrary spin is computed. To do so, we obtain the new expressions for tunneling rate, Hawking temperature and entropy of the black hole. At last, some comments are made on the results of our work.

Kerr–de Sitter and Kerr–anti–de Sitter black holes as accelerators for spinning particles

It is shown that the Kerr black hole could act as accelerators for spinning particles. In principle, it could obtain arbitrarily high energy for extremal Kerr black hole. In this paper, we extend the previous research to the Kerr-(anti-)de Sitter background and find that the cosmological constant plays an important role in the result. For the case of Kerr-anti-de Sitter black holes, like the Kerr background, only the extremal Kerr-anti-de Sitter black holes can have a divergent center-of-mass energy of collision. While, for the case of Kerr-de Sitter black holes, the collision of two spinning particles can take place on the outer horizon of the black holes and the center-of-mass energy of collision can blow up if one of the collision particle takes the critical angular momentum. Hence, non-extremal Kerr-de Sitter black holes could also act as accelerators with arbitrarily high center-of-mass energy for spinning particles.

Kerr-AdS analogue of triple point and solid/liquid/gas phase transition

We study the thermodynamic behavior of multi-spinning d = 6 Kerr-anti de Sitter black holes in the canonical ensemble of fixed angular momenta J1 and J2. We find, dependent on the ratio q = J2/J1, qualitatively different interesting phenomena known from the ‘every day thermodynamics’ of simple substances. For q = 0 the system exhibits recently observed reentrant large/small/large black hole phase transitions, but for 0 < q ≪ 1 we find an analogue of a ‘solid/liquid’ phase transition. Furthermore, for q ∈ (0.00905, 0.0985) the system displays the presence of a large/intermediate/small black hole phase transition with two critical and one triple (or tricritical) points. This behavior is reminiscent of the solid/liquid/gas phase transition except that the coexistence line of small and intermediate black holes does not continue for an arbitrary value of pressure (similar to the solid/liquid coexistence line) but rather terminates at one of the critical points. Finally, for q > 0.0985 we observe the ‘standard liquid/gas behavior’ of the Van der Waals fluid.

Entropy spectrum of a Kerr anti-de Sitter black hole

The entropy spectrum of a spherically symmetric black hole was derived without the quasinormal modes in the work of Majhi and Vagenas. Extending this work to rotating black holes, we quantize the entropy and the horizon area of a Kerr anti-de Sitter black hole by two methods. The spectra of entropy and area are obtained via the Bohr-Sommerfeld quantization rule and the adiabatic invariance in the first way. By addressing the wave function of emitted (absorbed) particles, the entropy and the area are quantized in the second one. Both results show that the entropy and the area spectra are equally spaced.

Particle acceleration in Kerr–(anti-)de Sitter black hole backgrounds

Banãdos, Silk and West (BSW) proved that Kerr black holes could act as particle accelerators with arbitrarily high center-of-mass energy, if two conditions are satisfied: (1) these black holes are extremal; (2) one of the colliding particles has critical angular momentum. In this paper, we extend the research to the cases of Kerr–(anti-)de Sitter black holes and find that the cosmological constant has an important effect on the result. In order for the case of Kerr–anti-de Sitter black holes (with negative cosmological constant) to get arbitrary high center-of-mass energy, we need an additional condition besides the above two for Kerr ones. While, for the case of general Kerr–de Sitter black holes (with positive cosmological constant), the collision of two particles can take place on the outer horizon of the black holes and the center-of-mass energy of collision can blow up arbitrarily if the above second condition is satisfied. Hence, non-extremal Kerr-de Sitter black holes could also act as particle accelerators with arbitrarily high center-of-mass energy.

Fermions tunneling of higher-dimensional Kerr–Anti-de Sitter black hole with one rotational parameter

The 1/2 spin fermions tunneling at the horizon of n-dimensional Kerr–Anti-de Sitter black hole with one rotational parameter is researched via semi-classical approximation method, and the Hawking temperature and fermions tunneling rate are obtained in this Letter. Using a new method, the semi-classical Hamilton–Jacobi equation is gotten from the Dirac equation in this Letter, and the work makes several quantum tunneling theories more harmonious.

Gyromagnetic ratio of charged Kerr–anti-de Sitter black holes

We examine the gyromagnetic ratios of rotating and charged AdS black holes in four and higher spacetime dimensions. We compute the gyromagnetic ratio for Kerr–AdS black holes with an arbitrary electric charge in four dimensions and show that it corresponds to g = 2 irrespective of the AdS nature of the spacetime. We also compute the gyromagnetic ratio for Kerr–AdS black holes with a single angular momentum and with a test electric charge in all higher dimensions. The gyromagnetic ratio crucially depends on the dimensionless ratio of the rotation parameter to the curvature radius of the AdS background. At the critical limit, when the boundary Einstein universe is rotating at the speed of light, it exhibits a striking feature leading to g = 2 regardless of the spacetime dimension. Next, we extend our consideration to include the exact metric for five-dimensional rotating charged black holes in minimal gauged supergravity. We show that the value of the gyromagnetic ratio found in the ‘test-charge’ approach remains unchanged for these black holes.

Thermodynamics and stability of higher dimensional rotating (Kerr-)AdS black holes

We study the thermodynamic and gravitational stability of Kerr anti-de Sitter black holes in five and higher dimensions. We show, in the case of equal rotation parameters, $a_i=a$, that the Kerr-AdS background metrics become stable, both thermodynamically and gravitationally, when the rotation parameters $a_i$ take values comparable to the AdS curvature radius. In turn, a Kerr-AdS black hole can be in thermal equilibrium with the thermal radiation around it only when the rotation parameters become not significantly smaller than the AdS curvature radius. We also find with equal rotation parameters that a Kerr-AdS black hole is thermodynamically favored against the existence of a thermal AdS space, while the opposite behavior is observed in the case of a single non-zero rotation parameter. The five dimensional case is however different and also special in that there is no high temperature thermal AdS phase regardless of the choice of rotation parameters. We also verify that at fixed entropy, the temperature of a rotating black hole is always bounded above by that of a non-rotating black hole, in four and five dimensions, but not in six and more dimensions (especially, when the entropy approaches zero or the minimum of entropy does not correspond to the minimum of temperature). In this last context, the six dimensional case is marginal.

The first law of thermodynamics for Kerr–anti-de Sitter black holes

We obtain expressions for the mass and angular momenta of rotating black holes in anti-de Sitter backgrounds in four, five and higher dimensions. We verify explicitly that our expressions satisfy the first law of thermodynamics, thus allowing an unambiguous identification of the entropy of these black holes with of the area. We find that the associated thermodynamic potential equals the background-subtracted Euclidean action multiplied by the temperature. Our expressions differ from many given in the literature. We find that in more than four dimensions, only our expressions satisfy the first law of thermodynamics. Moreover, in all dimensions we show that our expression for the mass coincides with that given by the conformal conserved charge introduced by Ashtekar, Magnon and Das. We indicate the relevance of these results to the AdS/CFT correspondence.

Small Kerr–anti-de Sitter black holes are unstable

Superradiance in black hole spacetimes can trigger instabilities. Here we show that, due to superradiance, small Kerr-anti-de Sitter black holes are unstable. Our demonstration uses a matching procedure, in a long wavelength approximation.

Entropy bound for a rotating system from anti–de Sitter black holes

General geodesic equations of the motion of spinning systems around the (3+1)-dimensional and (2+1)-dimensional rotating anti-de Sitter black holes have been obtained. Based upon these equations, we derived the entropy bound for a rotating system from Kerr-Anti de Sitter black holes and BTZ black holes, respectively. Our result coincides with that of Hod's derived from Kerr black hole, which shows that the entropy bound of the rotating system is neither dependent on the black hole parameters, nor on spacetime dimensions. It is a universal entropy bound.