Reissner Nordstrom Anti-de Sitter Black Hole Research Articles

The modified first laws of thermodynamics of anti-de Sitter and de Sitter space–times

We modify the first laws of thermodynamics of a Reissner–Nordstrom anti-de Sitter black hole and a pure de Sitter space–time by the surface tensions. The corresponding Smarr relations are obeyed. The cosmological constants are first treated as fixed constants, and then as variables associated to the pressures. For the black hole, the law is written as δE=TδS−σδA when the cosmological constant is fixed, where E is the Misner–Sharp mass and σ is the surface tension. Adopting the varied constant, we modify the law as δE0=TδS−σeffδA+VδP, where E0=M−Q22r+ is the enthalpy. The thermodynamical properties are investigated. For the de Sitter space–time, the expressions of the modified laws are different from these of the black hole. The differential way to derive the law is discussed.

The Thermodynamical Behaviors of Kerr—Newman AdS Black Holes

We reconsider the study of critical behaviors of Kerr—Newman Anti-de Sitter (AdS) black holes in four dimensions. The study is made in terms of the moduli space parameterized by the charge Q and the rotation parameter a, relating the mass M of the black hole and its angular momentum J via the relation a = J/M. Specifically, we discuss such thermodynamical behaviors in the presence of a positive cosmological constant considered as a thermodynamic pressure and its conjugate quantity as a thermodynamic volume. The equation of state for a charged Reissner—Nordstrom AdS black hole predicts a critical universal number depending on the (Q, a) moduli space. In the vanishing limit of the a parameter, this prediction recovers the usual universal number in four dimensions. Then, we find the bounded region of the moduli space allowing the consistency of the model with real thermodynamical variables.

Spectroscopy of the Reissner–Nordström–Anti-de Sitter Black Hole via Adiabatic Invariance

By combining the black hole property of adiabaticity and the oscillating velocity of the black hole horizon, we study the entropy and the area spectra of the Reissner–Nordstrom–anti-de Sitter black hole. Instead of using the quasi-normal mode frequencies, we utilize the oscillating velocity of the event horizon in the tunneling framework to obtain the black hole spectroscopy via adiabatic invariance. The results show that, both of the area spectrum and the entropy spectrum are equally spaced and independent on the parameters of the black hole.

Higher-dimensional chargedf(R)black holes

We construct a new class of higher-dimensional black hole solutions of $f(R)$ theory coupled to a nonlinear Maxwell field. In deriving these solutions the traceless property of the energy-momentum tensor of the matter filed plays a crucial role. In $n$-dimensional spacetime the energy-momentum tensor of conformally invariant Maxwell field is traceless provided we take $n=4p$, where $p$ is the power of conformally invariant Maxwell Lagrangian. These black hole solutions are similar to higher-dimensional Reissner-Nordstrom anti-de Sitter black holes but only exist for dimensions which are multiples of four. We calculate the conserved and thermodynamic quantities of these black holes and check the validity of the first law of black hole thermodynamics by computing a Smarr-type formula for the total mass of the solutions. Finally, we study the local stability of the solutions and find that there is indeed a phase transition for higher-dimensional $f(R)$ black holes with conformally invariant Maxwell source.

Tunneling Radiation Characteristic of the Charged Particle from the Reissner–Nordström–anti de Sitter Black Hole

Applying Parikh’s semi-classical quantum tunneling method, the tunneling radiation characteristic of the charged particle from the event horizon of the Reissner–Nordstrom–anti de Sitter black hole is researched. The result shows the derived spectrum is not purely thermal one, but is consistent with the underlying unitary theory, which gives a might explanation to the information loss paradox and is the correct amendment to the Hawking radiation.

Gravitational quasinormal modes for Kerr anti-de Sitter black holes

We investigate the quasinormal modes for gravitational perturbations of rotating black holes in four-dimensional anti-de Sitter (AdS) spacetime. The study of the quasinormal frequencies related to these modes is relevant to the AdS/CFT correspondence. Although results have been obtained for Schwarzschild and Reissner–Nordstrom AdS black holes, quasinormal frequencies of Kerr-AdS black holes are computed for the first time. We solve the Teukolsky equations in AdS spacetime, providing a second-order and a Padé approximation for the angular eigenvalues associated with the Teukolsky angular equation. The transformation theory and the Regge–Wheeler–Zerilli equations for Kerr-AdS are obtained.

On the classification of asymptotic quasinormal frequencies for {$d$}-dimensional black holes and quantum gravity

We provide a complete classification of asymptotic quasinormal frequencies for static, spherically symmetric black hole spacetimes in d dimensions. This includes all possible types of gravitational perturbations (tensor, vector and scalar type) as described by the Ishibashi–Kodama master equations. The frequencies for Schwarzschild are dimension independent, while for Reissner–Nordstrom are dimension dependent (the extremal Reissner–Nordstrom case must be considered separately from the non–extremal case). For Schwarzschild de Sitter, there is a dimension independent formula for the frequencies, except in dimension d = 5 where the formula is different. For Reissner–Nordstrom de Sitter there is a dimension dependent formula for the frequencies, except in dimension d = 5 where the formula is different. Schwarzschild and Reissner–Nordstrom Anti–de Sitter black hole spacetimes are simpler: the formulae for the frequencies will depend upon a parameter related to the tortoise coordinate at spatial infinity, and scalar type perturbations in dimension d = 5 lead to a continuous spectrum for the quasinormal frequencies. We also address non–black hole spacetimes, such as pure de Sitter spacetime—where there are quasinormal modes only in odd dimensions—and pure Anti–de Sitter spacetime—where again scalar type perturbations in dimension d = 5 lead to a continuous spectrum for the normal frequencies. Our results match previous numerical calculations with great accuracy. Asymptotic quasinormal frequencies have also been applied in the framework of quantum gravity for black holes. Our results show that it is only in the simple Schwarzschild case which is possible to obtain sensible results concerning area quantization or loop quantum gravity. In an effort to keep this paper self–contained we also review earlier results in the literature.