Charged Kerr Black Hole Research Articles

Charged Particle Circular Orbits around Weakly Charged and Magnetized Kerr Black Holes

We study the circular orbits of charged particles around a weakly charged Kerr black hole immersed in a weak, axisymmetric magnetic field. First, we review the circular orbits of neutral particles. We then review the circular orbits of charged particles around a weakly charged Kerr black hole and weakly magnetized Kerr black hole. The case of a weakly magnetized and charged black hole is investigated thereafter. We investigate, in particular, the effect of the electromagnetic forces on the charged particles’ innermost stable circular orbits. We examine the conditions for the existence of negative-energy stable circular orbits and the possibility of the emergence of a gap or double orbit in thin accretion disks. Some of the interesting astrophysical consequences of our findings are discussed as well.

Hawking Radiation from Charged Kerr Black Hole Beyond Semi-classical Approximation

The Hawking radiation from charged Kerr black hole via the method beyond semi-classical approximation is studied. In our work, we apply the WKB approximation method and the quantum tunneling method, then calculate the tunneling rate and further correct Hawking entropy to charged Kerr black hole. It is shown that the result is still in agreement with the unitary theory, the entropy of the black hole contains three parts: the usual Bekenstein-Hawking entropy, the logarithmic term and the inverse area term. Apart from coefficients, our correction to the charged Kerr black hole entropy is consistent with results of loop quantum gravity.

Hawking temperature from the charged Kerr black hole in five dimension via fermions tunneling method

In this paper, motivated by fermions tunneling method of 4 dimensional black holes, we extend the analysis to the charged Kerr black hole in five dimension by constructing a set of appropriate matrices γμ for general covariant Dirac equation. As a result, we successfully recover the expected Hawking temperature.

Hawking radiation as quantum tunneling in Rindler coordinate

We substantiate the Hawking radiation as quantum tunneling of fields or particles crossing the horizon by using the Rindler coordinate. The thermal spectrum detected by an accelerated particle is interpreted as quantum tunneling in the Rindler spacetime. Representing the spacetime near the horizon locally as a Rindler spacetime, we find the emission rate by tunneling, which is expressed as a contour integral and gives the correct Boltzmann factor. We apply the method to non-extremal black holes such as a Schwarzschild black hole, a non-extremal Reissner-Nordstrom black hole, a charged Kerr black hole, a de Sitter space, and a Schwarzschild-anti de Sitter black hole.

Charged Black Holes: Wave Equations for Gravitational and Electromagnetic Perturbations

A pair of wave equations for the electromagnetic and gravitational perturbations of the charged Kerr black hole are derived. The perturbed Einstein-Maxwell equations in a new gauge are employed in the derivation. The wave equations refer to the perturbed Maxwell spinor $\Phi_0$ and to the shear $\sigma$ of a principal null direction of the Weyl curvature. The whole construction rests on the tripod of three distinct derivatives of the first curvature $\kappa$ of a principal null direction.

Nonvanishing magnetic flux through the slightly charged Kerr black hole

In association with the Blanford-Znajek mechanism for rotational energy extraction from Kerr black holes, it is of some interest to explore how much of magnetic flux can actually penetrate the horizon at least in idealized situations. For completely uncharged Kerr hole case, it has been known for some time that the magnetic flux gets entirely expelled when the hole is maximally-rotating. In the mean time, it is known that when the rotating hole is immersed in an originally uniform magnetic field surrounded by an ionized interstellar medium (plasma), which is a more realistic situation, the hole accretes certain amount of electric charge. In the present work, it is demonstrated that as a result of this accretion charge small enough not to disturb the geometry, the magnetic flux through this slightly charged Kerr hole depends not only on the hole's angular momentum but on the hole's charge as well such that it never vanishes for any value of the hole's angular momentum.

Electromagnetic energy for a charged Kerr black hole in a uniform magnetic field

With the Komar mass formula we calculate the electromagnetic energy for a charged Kerr black hole in a uniform magnetic field. We find that the total electromagnetic energy takes the minimum when the Kerr black hole possesses a nonzero net charge $Q=2\ensuremath{\xi}{B}_{0}{J}_{H}$ where ${B}_{0}$ is the strength of the magnetic field, ${J}_{H}$ is the angular momentum of the black hole, and $\ensuremath{\xi}$ is a dimensionless parameter determined by the spin of the black hole. However, the Wald state with ${Q=2B}_{0}{J}_{H}$ does not minimize the electromagnetic energy.

Quasilocal energy for rotating charged black hole solutions in general relativity and string theory

We explore the (non)-universality of Martinez's conjecture, originally proposed for Kerr black holes, within and beyond general relativity. The conjecture states that the Brown-York quasilocal energy at the outer horizon of such a black hole reduces to twice its irreducible mass, or equivalently, to \sqrt{A} /(2\sqrt{pi}), where `A' is its area. We first consider the charged Kerr black hole. For such a spacetime, we calculate the quasilocal energy within a two-surface of constant Boyer-Lindquist radius embedded in a constant stationary-time slice. Keeping with Martinez's conjecture, at the outer horizon this energy equals the irreducible mass. The energy is positive and monotonically decreases to the ADM mass as the boundary-surface radius diverges. Next we perform an analogous calculation for the quasilocal energy for the Kerr-Sen spacetime, which corresponds to four-dimensional rotating charged black hole solutions in heterotic string theory. The behavior of this energy as a function of the boundary-surface radius is similar to the charged Kerr case. However, we show that in this case it does not approach the expression conjectured by Martinez at the horizon.

Conical geometry and quantum entropy of a charged Kerr black hole.

We apply the method of conical singularities to calculate the tree-level entropy and its one-loop quantum corrections for a charged Kerr black hole. The Euclidean geometry for the Kerr-Newman metric is considered. We show that for an arbitrary periodization in Euclidean space there exists a conical singularity at the horizon. Its $\delta$-function like curvatures are calculated and are shown to behave similar to the static case. The heat kernel expansion for a scalar field on this conical space background is derived and the (divergent) quantum correction to the entropy is obtained. It is argued that these divergences can be removed by renormalization of couplings in the tree-level gravitational action in a manner similar to that for a static black hole.

The entropy of a quantum field in a charged Kerr black hole

We calculate the entropies of a system of classical particles and a quantum scalar field by using the brick wall method in a thermal bath in a charged Kerr black hole spacetime. The leading terms at the Hartle-Hawking temperature T H = κ 2π are given by S cl ≈ N In( A b ϵ 2 ) , and S ≈ N′ A H ϵ 2 , where A b and A H are the area of the box and the horizon, respectively.

Axisymmetric quasistationary stability of a charged Kerr black hole

Axisymmetric quasistationary stability of a charged Kerr black hole

Electromagnetic radiation generated by gravitational perturbations of a charged rotating black hole

Gravitational perturbations on a mildly charged Kerr black hole are analyzed. These perturbations distort the static electromagnetic field to give rise to electromagnetic radiation. A wave equation for the electromagnetic radiation is derived in the Newman-Penrose formalism.

Stationary, axially symmetric perturbations of charged Kerr black holes

It is proved that the only admissible time-independent, axially symmetric perturbations around a charged Kerr black hole are those which correspond to adding charge, mass, and angular momentum to the black hole.

Surface Geometry of Charged Rotating Black Holes

Invariant measures of the surface geometry of a charged rotating (Kerr-Newman) black hole are examined. It is shown that as the rotation rate of the black hole increases, the equatorial circumference increases while the polar circumference decreases. This is analogous to effects in material rotating bodies. The number of parameters describing a charged Kerr black hole drops from three to two on its surface. It is found that a scale parameter $\ensuremath{\eta}$ and a distortion parameter $\ensuremath{\beta}$ describe this geometry very simply. There emerge two classes of Kerr metrics separated by $\ensuremath{\beta}=\frac{1}{2}$. For larger $\ensuremath{\beta}$ the Gaussian curvature becomes negative on two polar-cap regions and the surface cannot be globally embedded in Euclidean 3-space. Possible physical effects are briefly discussed.