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Register a new userKappa - Poincare dispersion relations and the black hole radiation
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Following the methods developed by Corley and Jacobson, we consider qualitatively the issue of Hawking radiation in the case when the dispersion relation is dictated by quantum kappa-Poincare algebra. This relation corresponds to field equations that are non-local in time, and, depending on the sign of the parameter kappa, to sub- or superluminal signal propagation. We also derive the conserved inner product, that can be used to count modes, and therefore to obtain the spectrum of black hole radiation in this case.
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We use our previously developed identification of dispersion relations with Hamilton functions on phase space to locally implement the $kappa$-Poincare dispersion relation in the momentum spaces at each point of a generic curved spacetime. We use this general construction to build the most general Hamiltonian compatible with spherical symmetry and the Plank-scale-deformed one such that in the local frame it reproduces the $kappa$-Poincare dispersion relation. Specializing to Planck-scale-deformed Schwarzschild geometry, we find that the photon sphere around a black hole becomes a thick shell since photons of different energy will orbit the black hole on circular orbits at different altitudes. We also compute the redshift of a photon between different observers at rest, finding that there is a Planck-scale correction to the usual redshift only if the observers detecting the photon have different masses.
We study noncommutative deformations of the wave equation in curved backgrounds and discuss the modification of the dispersion relations due to noncommutativity combined with curvature of spacetime. Our noncommutative differential geometry approach is based on Drinfeld twist deformation, and can be implemented for any twist and any curved background. We discuss in detail the Jordanian twist $-$giving $kappa$-Minkowski spacetime in flat space$-$ in the presence of a Friedman-Lema^{i}tre-Robertson-Walker (FLRW) cosmological background. We obtain a new expression for the variation of the speed of light, depending linearly on the ratio $E_{ph}/E_{LV}$ (photon energy / Lorentz violation scale), but also linearly on the cosmological time, the Hubble parameter and inversely proportional to the scale factor.
Stimulated emission by black holes is discussed in light of the analogue gravity program. We first consider initial quantum states containing a definite number of particles, and then we take into account the case where the initial state is a coherent state. The latter case is particularly significant in the case where Hawking radiation is studied in dielectric black holes, and the emission is stimulated by a laser probe. We are particularly interested in the case of the electromagnetic field, for which stimulated radiation is calculated too.
We compute the scattering cross section of Reissner-Nordstrom black holes for the case of an incident electromagnetic wave. We describe how scattering is affected by both the conversion of electromagnetic to gravitational radiation, and the parity-dependence of phase shifts induced by the black hole charge. The latter effect creates a helicity-reversed scattering amplitude that is non-zero in the backward direction. We show that from the character of the electromagnetic wave scattered in the backward direction it is possible, in principle, to infer if a static black hole is charged.
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.
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