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Register a new userNoncommutative Reissner-Nordstr{o}m Black hole
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A deformed embedding of the Reissner-Nordstr{o}m spacetime is constructed within the framework of a noncommutative Riemannian geometry. We find noncommutative corrections to the usual Riemannian expressions for the metric and curvature tensors, which, in the case of the metric, are valid to all orders in the deformation parameter. We calculate the area of the event horizon of the corresponding noncommutative R-N black-hole, obtaining corrections up to fourth order in the deformation parameter for the area of the black-hole. Finally we include some comments on the noncommutative version on one of the second order scalar invariants of the Riemann tensor, the so called Kretschmann invariant, a quantity regularly used in order to extend gravity to quantum level.
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We obtain an analytic solution for accretion of a gaseous medium with a adiabatic equation of state ($P=rho$) onto a Reissner-Nordstr{o}m black hole which moves at a constant velocity through the medium. We obtain the specific expression for each component of the velocity and present the mass accretion rate which depends on the mass and the electric charge. The result we obtained may be helpful to understand the physical mechanism of accretion onto a moving black hole.
Banerjee and Majhis recent work shows that black holes emission spectrum could be fully reproduced in the tunneling picture, where, as an intriguing technique, the Kruskal extension was introduced to connect the left and right modes inside and outside the horizon. Some attempt, as an extension, was focused on producing the Hawking emission spectrum of the (charged) Reissner-Nordstr{o}m black hole in the Banerjee-Majhis treatment. Unfortunately, the Kruskal extension in their observation was so badly defined that the ingoing mode was classically forbidden traveling towards the center of black hole, but could quantum tunnel across the horizon with the probability $Gamma=e^{-pi omega_0/kappa_+}$. This tunneling picture is unphysical. With this point as a central motivation, in this paper we first introduce such a suitable Kruskal extension for the (charged) Reissner-Nordstr{o}m black hole that a perfect tunneling picture can be provided during the charged particles emission. Then, under the new Kruskal extension, we revisit the Hawking emission spectrum and entropy spectroscopy as tunneling from the charged black hole. The result shows that the tunneling method is so universally robust that the Hawking blackbody emission spectrum from a charged black hole can be well reproduced in the tunneling mechanism, and its induced entropy quantum is a much better approximation for the forthcoming quantum gravity theory.
We present the analytical post-Newtonian solutions for the test particles motion in the Reissner-Nordstr{o}m spacetime. The solutions are formulated in the Wagoner-Will representation, the Epstein-Haugan representation, the Brumberg representation, and the Damour-Deruelle representation, respectively. The relations between the (post-)Keplerian parameters in different representations, as well as their relations to the orbital energy and angular momentum are also provided.
For the Schwarzschild black hole the Bekenstein-Hawking entropy is proportional to the area of the event horizon. For the black holes with two horizons the thermodynamics is not very clear, since the role of the inner horizons is not well established. Here we calculate the entropy of the Reissner-Nordstrom black hole and of the Kerr black hole, which have two horizons. For the spherically symmetric Reissner-Nordstrom black hole we used several different approaches. All of them give the same result for the entropy and for the corresponding temperature of the thermal Hawking radiation. The entropy is not determined by the area of the outer horizon, and it is not equal to the sum of the entropies of two horizons. It is determined by the correlations between the two horizons, due to which the total entropy of the black hole and the temperature of Hawking radiation depend only on mass $M$ of the black hole and do not depend on the black hole charge $Q$. For the Kerr and Kerr-Newman black holes it is shown that their entropy has the similar property: it depends only on mass $M$ of the black hole and does not depend on the angular momentum $J$ and charge $Q$.
We investigate spherically symmetric, steady state, adiabatic accretion onto a Tangherlini-Reissner-Nordstrom black hole in arbitrary dimensions by using $D$-dimensional general relativity. We obtain basic equations for accretion and determine analytically the critical points, the critical fluid velocity, and the critical sound speed. We lay emphasis on the condition under which the accretion is possible. This condition constrains the ratio of mass to charge in a narrow limit, which is independent of dimension for large dimension. This condition may challenge the validity of the cosmic censorship conjecture since a naked singularity is eventually produced as the magnitude of charge increases compared to the mass of black hole.
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