Despite over thirty years of research in black hole thermodynamics, our understanding of the possible role played by the inner horizons of Reissner–Nordström 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–Nordström black hole. As a result, we find that in a maximally extended Reissner–Nordström space–time virtual particle–antiparticle pairs are created at the inner horizon of the Reissner–Nordström 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 be emitted from the white hole horizon in the maximally extended Reissner–Nordström space–time, 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 radition effects of black hole horizons, the white hole horizon also 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–Nordström black hole.
Quantum effects near the Cauchy horizon of a Reissner-Nordström black hole
