Reissner-Nordstrom Black Hole Spacetime Research Articles

Effective Geometry of the Bardeen Spacetimes: Gravitational Lensing and Frequency Mapping of Keplerian Disks

Abstract We study the appearance of Keplerian accretion disks in order to demonstrate the influence of the nonlinear electrodynamics (NED) on the gravitational lensing and frequency shifting of the images of the Keplerian disks. We focus our attention on the Bardeen black hole backgrounds with magnetic charges that could be considered to be acceptable solutions for the Einstein gravitational equations combined with those representing an NED. Photons governing the appearance of the Keplerian disks follow null geodesics of the effective geometry related to the Bardeen spacetime. We compare the appearance governed by the effective geometry to those governed by the spacetime geometry itself, and to the appearance of Keplerian disks orbiting a related Reissner–Nordstrom black hole spacetime. We demonstrate a clear and very strong difference between the disk images determined by the effective geometry and the others, both in the shape and (especially) in the frequency mapping where it exhibits a difference of three orders.

Statistical Entropy of Dirac Field Outside RN Black Hole and Modified Density Equation

Statistical entropy of Dirac field in Reissner–Nordstrom black hole space-time is computed by state density equation corrected by the generalized uncertainty principle to all orders in Planck length and WKB approximation. The result shows that the statistical entropy is proportional to the horizon area but the present result is convergent without any artificial cutoff.

Foliation and the First Law of Black Hole Thermodynamics

There has been lots of interest in exploring the thermodynamic properties at the horizon of a black hole spacetime. It has been shown earlier that for different spacetimes, the Einstein field equations at the horizon can be expressed as the first law of black hole thermodynamics. Using the idea of foliation, we develop a simpler procedure to obtain such results. We consider r = constant slices, for the Schwarzschild and Reissner—Nordstrom black hole spacetimes. The Einstein field equations for the induced 3-dimensional metrics of the hypersurfaces are expressed in thermodynamic quantities under the virtual displacements of the hypersurfaces. As expected, it is found that the field equations of the induced metric corresponding to the horizon can be written as a first law of black hole thermodynamics. It is to be mentioned here that our procedure is much easier, to obtain such results, as here one has to essentially deal with (n — 1)-dimensional induced metric for an n-dimensional spacetime.

Foliation of the Kottler–Schwarzschild–de Sitter spacetime by flat spacelike hypersurfaces

There exist Kruskal like coordinates for the Reissner–Nordstrom (RN) black hole spacetime which are regular at coordinate singularities. Non-existence of such coordinates for the extreme RN black hole spacetime has already been shown. Also the Carter coordinates available for the extreme case are not manifestly regular at the coordinate singularity, therefore, a numerical procedure was developed to obtain free fall geodesics and flat foliation for the extreme RN black hole spacetime. The Kottler–Schwarzschild–de Sitter (KSSdS) spacetime geometry is similar to the RN geometry in the sense that, like the RN case, there exist non-singular coordinates when there are two distinct coordinate singularities. There are no manifestly regular coordinates for the extreme KSSdS case. In this paper foliation of all the cases of the KSSdS spacetime by flat spacelike hypersurfaces is obtained by introducing a non-singular time coordinate.