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Register a new userScalar radiation emitted from a rotating source around a Reissner-Nordstrom black hole
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Added by
Andr\\'e da Silva Ricardo Rocha
Publication date
2008
fields
Physics
and research's language is
English
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We investigate the radiation emitted from a scalar source in circular orbit around a Reissner-Nordstrom black hole. Particle and energy emission rates are analytically calculated in the low- and high-frequency regimes and shown to be in full agreement with a numerical calculation. Our investigation is connected with the recent discussion on the validity of the cosmic censorship conjecture in the quantum realm.
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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.
Despite of over thirty years of research of the black hole thermodynamics our understanding of the possible role played by the inner horizons of Reissner-Nordstrom and Kerr-Newman black holes in black hole thermodynamics is still somewhat incomplete: There are derivations which imply that the temperature of the inner horizon is negative and it is not quite clear what this means. Motivated by this problem we perform a detailed analysis of the radiation emitted by the inner horizon of the Reissner-Nordstrom black hole. As a result we find that in a maximally extended Reissner-Nordstrom spacetime virtual particle-antiparticle pairs are created at the inner horizon of the Reissner-Nordstrom black hole such that real particles with positive energy and temperature are emitted towards the singularity from the inner horizon and, as a consequence, antiparticles with negative energy are radiated away from the singularity through the inner horizon. We show that these antiparticles will come out from the white hole horizon in the maximally extended Reissner-Nordstrom spacetime, at least when the hole is near extremality. The energy spectrum of the antiparticles leads to a positive temperature for the white hole horizon. In other words, our analysis predicts that in addition to the radiation effects of black hole horizons, also the white hole horizon radiates. The black hole radiation is caused by the quantum effects at the outer horizon, whereas the white hole radiation is caused by the quantum effects at the inner horizon of the Reissner-Nordstrom black hole.
We study the interior of a Reissner-Nordstrom Black-Hole (RNBH) using Relativistic Quantum Geometry, which was introduced in some previous works. We found discrete energy levels for a scalar field from a polynomial condition for the Heun Confluent functions expanded around the effective causal radius $r_*$. From the solutions it is obtained that the uncertainty principle is valid for each energy level of space-time, in the form: $E_n, r_{*,n}=hbar/2$, and the charged mass is discretized and distributed in a finite number of states. The classical RNBH entropy is recovered as the limit case where the number of states is very large, and the RNBH quantum temperature depends on the number of states in the interior of the RNBH. This temperature, depending of the number of states of the RNBH, is related with the Bekeinstein-Hawking (BH) temperature: $T_{BH} leq T_{N} < 2,T_{BH}$.
In this work, we investigate the Hawking radiation in higher dimensional Reissner-Nordstrom black holes as received by an observer, resides at infinity. The frequency-dependent transmission rates, which deform the thermal radiation emitted in the vicinity of the black hole horizon, are evaluated numerically. Apart from the case of four-dimensional spacetime, the calculations are extended to higher dimensional Reissner-Nordstrom metrics, and the results are found to be somewhat sensitive to the spacetime dimension. In general, it is observed that the transmission coefficients practically vanishes when the frequency of the emitted particle approaches zero. It increases with increasing frequency and eventually saturates to some value. For four-dimensional spacetime, the above result is shown to be mostly independent of the metrics parameter, neither of the orbital quantum number of the particle, once the location of the event horizon, $r_h$, and the product of the charges of the black hole and the particle $qQ$ are given. For higher-dimensional cases, on the other hand, the convergence becomes more slowly. Moreover, the difference between states with different orbital quantum numbers is found to be more significant. As the magnitude of the product of charges $qQ$ becomes more significant, the transmission coefficient exceeds one. In other words, the resultant spectral flux is amplified, which results in an accelerated process of black hole evaporation. The relation between the calculated outgoing transmission coefficient with existing results on the greybody factor is discussed.
We derive explicit expressions for the two-point function of a massless scalar field in the interior region of a Reissner-Nordstrom black hole, in both the Unruh and Hartle-Hawking quantum states. The two-point function is expressed in terms of the standard $lmomega$ modes of the scalar field (those associated with a spherical harmonic $Y_{lm}$ and a temporal mode $e^{-iomega t}$), which can be conveniently obtained by solving an ordinary differential equation, the radial equation. These explicit expressions are the internal analogs of the well known results in the external region (originally derived by Christensen and Fulling), in which the two-point function outside the black hole is written in terms of the external $lmomega$ modes of the field. They allow the computation of $<Phi^{2}>_{ren}$ and the renormalized stress-energy tensor inside the black hole, after the radial equation has been solved (usually numerically). In the second part of the paper, we provide an explicit expression for the trace of the renormalized stress-energy tensor of a minimally-coupled massless scalar field (which is non-conformal), relating it to the dAlembertian of $<Phi^{2}>_{ren}$. This expression proves itself useful in various calculations of the renormalized stress-energy tensor.
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