Static Charged Black Holes Research Articles

Extremal static AdS black hole/CFT correspondence in gauged supergravities

A recently proposed holographic duality allows the Bekenstein–Hawking entropy of extremal rotating black holes to be calculated microscopically, by applying the Cardy formula to the two-dimensional chiral CFTs associated with certain reparameterisations of azimuthal angular coordinates in the solutions. The central charges are proportional to the angular momenta of the black hole, and so the method degenerates in the case of static (non-rotating) black holes. We show that the method can be extended to encompass such charged static extremal AdS black holes by using consistent Kaluza–Klein sphere reduction ansatze to lift them to exact solutions in the low-energy limits of string theory or M-theory, where the electric charges become reinterpreted as angular momenta associated with internal rotations in the reduction sphere. We illustrate the procedure for the examples of extremal charged static AdS black holes in four, five, six and seven dimensions.

On five-dimensional non-extremal charged black holes and FRW cosmology

We consider static non-extremal charged black hole solutions in the context of N = 2 gauged supergravity theories in five dimensions, and we show that they satisfy first-order flow equations. Then we analyze the motion of the dual brane in these black hole backgrounds. We express the entropy in terms of a Cardy–Verlinde-type formula, and we show that the equations describing the FRW cosmology on the brane have a form that is similar to the equations for the entropy and for the Casimir energy on the brane. We also briefly comment on the inclusion of a Gauss–Bonnet term in the analysis.

Superradiance and Instability of Black Holes

The stability of black holes has a crucial importance when we study their formation and fate in Nature. It also has an intimate relation with the cosmic censorship hypothesis. For these reasons, this problem has been studied for a long time, and uniqueness and perturbative stability were established for most asymptotically flat black holes in the four-dimensional Einstein-Maxwell system except for the KerrNewman black hole. 1),2) When we go beyond this classical system, we encounter various new situations. One such extension is to consider systems containing other types of matter. Very interesting examples are the Einstein-Skyrme system and the Einstein-Yang-Mills system. These systems have three families of static asymptotically flat spherically symmetric solutions; a soliton family, a hairy black hole family and the vacuum one. These all families of solutions were shown to be stable numerically for the EinsteinSkyrme system while for the EYM system, the colored black holes and the soliton solutions were shown to be unstable (see Ref. 3) for review). Hence, in the latter case, the uniqueness theorem holds practically. Another extension motivated by recent progresses in unified theories is to consider higher-dimensional black holes. In the static AF Einstein-Maxwell system, the uniqueness theorem still holds in higher dimensions. Further, in the vacuum case, the Schwarzschild-Tangherlini solution was shown to be stable 4) by using the extension of the Regge-Wheeler and Zerilli equations to higher dimensions, 5) although the stability of the charged static black hole was proved only for D = 5 analytically 6) and for 6 ≤ D ≤ 11 numerically. 7)

STATIC CHARGED DILATON BLACK HOLE SOLUTIONS IN NON-COMMUTATIVE SPACES

Here we consider the black hole solutions which were obtained by Chan and Mann.1 These solutions represent static charged black holes with a dilaton field. Then we compute the corrections to the horizons and Hawking temperature of these black holes. These corrections stem from the space non-commutativity. We show that in a non-commutative case, temperature of extreme black hole, in contrast to that of the commutative case, is not zero.

Stability and Quasi Normal Modes of Charged Born–Infeld Black Holes

In this paper we study the stability and quasi-normal modes of scalar perturbations of black holes. The static charged black hole considered here is a solution to Born-Infeld electrodynamics coupled to gravity. We conclude that the black hole is stable. We also compare the stability of it with its linear counter-part Reissner-Nordstrom black hole. The quasi-normal modes are computed using the WKB method. The behavior of these modes with the non-linear parameter, temperature, mass of the scalar field and the spherical index are analyzed in detail.

Kaluza-Klein Black Holes with Squashed Horizons

We study geometrical structures of charged static black holes in the five-dimensional Einstein-Maxwell theory. The black holes we study have horizons in the form of squashed $ {\rm S}^3$, and their asymptotic structure consists of a twisted ${\rm S}^1$ bundle over the four-dimensional flat spacetime at the spatial infinity. The spacetime we consider is fully five-dimensional in the vicinity of the black hole and four-dimensional with a compact extra dimension at infinity.

Classification of static charged black holes in higher dimensions

The uniqueness theorem for a static charged higher dimensional black hole containing an asymptotically flat spacelike hypersurface with compact interior and with both degenerate and nondegenerate components of event horizon is proposed. By studies of the near-horizon geometry of degenerate horizons, one was able to eliminate the previous restriction concerning the inequality fulfilled by the charges of the adequate components of the aforementioned horizons.

Evolution of a self-interacting scalar field in the spacetime of a higher dimensional black hole

In the spacetime of n-dimensional static charged black hole we examine the mechanism by which the self-interacting scalar hair decay. It is turned out that the intermediate asymptotic behavior of the self-interacting scalar field is determined by an oscillatory inverse power law. We confirm our results by numerical calculations.

Birkhoff’s theorem in Lovelock gravity

We show that the solutions of the Lovelock equations with spherical, planar, or hyperbolic symmetry are locally isometric to the corresponding static Lovelock black hole. As a consequence, these solutions are locally static: they admit an additional Killing vector that can either be space-like or time-like, depending on the position. This result also holds in the presence of an abelian gauge field, in which case the solutions are locally isometric to a charged static black hole.

Scalar Perturbations of Charged Dilaton Black Holes

We have studied the scalar perturbation of static charged dilaton black holes in 3+1 dimensions. The black hole considered here is a solution to the low-energy string theory in 3+1 dimensions. The quasinormal modes for the scalar perturbations are calculated using the third order WKB method. The dilaton coupling constant has a considerable effect on the values of quasi normal modes. It is also observed that there is a linear relation between the quasi normal modes and the temperature for large black holes.

Quasinormal Modes of Charged Dilaton Black Holes in 2 + 1 Dimensions

We have studied the scalar perturbation of static charged dilaton black holes in 2 + 1 dimensions. The black hole considered here is a solution to the low-energy string theory in 2 + 1 dimensions. It is asymptotic to the anti-de Sitter space. The exact values of quasinormal modes for the scalar perturbations are calculated. For both the charged and uncharged cases, the quasinormal frequencies are pure-imaginary leading to purely damped modes for the perturbations.

Stress-energy tensor for a massless spin 1/2 field in static black hole spacetimes.

The stress-energy tensor for the massless spin 1/2 field is numerically computed outside and on the event horizons of both charged and uncharged static nonrotating black holes, corresponding to the Schwarzschild, Reissner-Nordström, and extreme Reissner-Nordström solutions of Einstein's equations. The field is assumed to be in a thermal state at the black hole temperature. Comparison is made between the numerical results and previous analytic approximations for the stress-energy tensor in these spacetimes. For the Schwarzschild (charge zero) solution, it is shown that the stress energy differs even in sign from the analytic approximation. For the Reissner-Nordström and extreme Reissner-Nordström solutions, divergences predicted by the analytic approximations are shown not to exist.

Geodesic Structure of Static Charged Black Hole Solutions in 2 + 1 Dimensions

Geodesics structure of static charged black holes for dilaton gravity is constructed. In particular, circular and radial geodesics for charged and uncharged test particles are studied. Various possibilities are discussed for range of parameters for the black hole and the test particles. The orbits of the particles with angular momentum are presented.

Uniqueness theorem of static degenerate and nondegenerate charged black holes in higher dimensions

We prove the uniqueness theorem for static higher dimensional charged black holes spacetime containing an asymptotically flat spacelike hypersurface with compact interior and with both degenerate and non-degenerate components of the event horizon.

Adjoint operators, gauge invariant perturbations, and covariant symplectic form for black holes in string theory

Using a scheme of adjoint operators, we give a covariant and gauge invariant treatment for the perturbation theory of static charged black holes in string theory, valid for curvature below the Planck scale; conserved quantities and a covariant symplectic form on the phase space are explicitly constructed. Future extensions of the present results are discussed.

Quasilocal Energy for Static Charged Black Holes in String Theory

The Brown–York quasilocal energies of some static charged dilaton black holes are calculated, and then the validity of Martinez's conjecture is explored in string theory. It is shown that the energy is positive and monotonically decreases to the ADM mass at spatial infinity, and the conjecture that the Brown–York quasilocal energy at the outer horizon of black hole reduces to twice of its irreducible mass is still applicable for the static charged black holes in string theory. The result is different from Bose–Naing's one.

Evaporation of a two-dimensional charged black hole

We construct a dilatonic two-dimensional model of a charged black hole. The classical solution is a static charged black hole, characterized by two parameters m and q representing the black hole's mass and charge. Then we study the semiclassical effects, and calculate the evaporation rate of both m and q, as a function of these two quantities. Analyzing this dynamical system, we find two qualitatively different regimes, depending on the electromagnetic coupling constant ${g}_{A}.$ If the latter is greater than a certain critical value, the charge-to-mass ratio decays to zero upon evaporation. On the other hand, for ${g}_{A}$ smaller than the critical value, the charge-to-mass ratio approaches a non-zero constant that depends on ${g}_{A}$ but not on the initial values of m and q.

LETTER: Newman–Janis Method and Rotating Dilaton-Axion Black Hole

It is shown that the dilaton-axion rotating black hole solution can be obtained from GGHS static charged dilaton black hole solution via the Newman–Janis method.

On the equilibrium of charged masses in general relativity: the electrostatic case

The problem of the equilibrium of charged aligned masses is discussed within the framework of the electrostatic multi-soliton solution of the Einstein-Maxwell equations. The equilibrium states in a charged two-body system are considered in detail. We demonstrate the validity of Smarr's mass formula for a charged static black hole when the latter is in electrostatic equilibrium with a superextreme object.

Thermodynamics of a Static Dilaton Black Hole

The thermodynamics of a static dilaton black hole is investigated by Euclidean path integral. Four interesting results are obtained: (I) Although the temperature, heat capacity and chemical potential have diferent forms as compared to general classical static charged black hole, the Bardeen-Carter-Hawking thermodynamical laws are valid for the black hole. (II) The entropy and area of the event horizon are zero but the energy, temperature and surface gravity are non-zero for extremal case (rh = 2M = b). (III) The charged black hole does not possess second order phase transitions as the Reissner-Nordström black hole since its heat capacity is negative. (IV) The action is equal to the entropy, and both quantities coincide with one quarter of area of the event horizon.