Evolution of charged evaporating black holes

Abstract

The evaporative evolution of charged nonrotating black holes is studied by numerically integrating a set of coupled differential equations describing the charge and mass as functions of time. We find that large charged black holes will evolve through a region (in the black-hole configuration space) of positive specific heat, undergoing two phase transitions as they evaporate. The region is approximately bounded by a < ( Q / M )~ < 1 and M > 2.03X 1 0 '~~. Unlike rotating black holes (which always evolve toward the Schwarzschild limit), sufficiently large charged black holes will initially evolve toward the extreme Reissner-Nordstrom limit; their lifetime may be many orders of magnitude larger than the lifetime of a Schwarzschild black hole with the same initial mass.

Spontaneous loss of charge of the Reissner-Nordström black hole

“…This shows that the loss of charge process of the hole is described by Schwinger effect, as in ordinary flat-space quantum eletrodynamics. This result can be understood by noting that in the large radius hypothesis adopted above, the event horizon of the hole is much larger than the Compton wavelength of the emitted particles, and the radiated pairs can be viewed as being produced by the electic field of the hole, and not by the gravitational field [7]. Our result is compatible with the usual rate of electron-positron pair creation; indeed, remember that we obtained it in a reduced 1+1 dimensional spacetime.…”

“…They spontaneously radiate their own charge and, once they are neutralized, continue to evaporate according to the usual Hawking process. On the other hand, for the same Q/M ratio charge, the holes more massive lose mass by the Hawking process, while they conserve the same electric charge (the most massive even become "extreme"), before that the neutralization process really happens [7].…”

“…In order to describe the evaporation scenarii for the charged black holes, a more detailed analysis is needed [7], because the holes also radiate neutral particles with a thermal rate.…”

Renormalization of the charged scalar field in curved space

“…Hiscock and Weems [19] considered the loss of charge and mass for the exteriors of charged black holes of large initial mass. They assumed adiabatic evolution, so that the spacetime could be described by a sequence of Reissner-Nordström metrics with the mass and charge of the black hole being slowly varying functions of time.…”

Effects of nonzero neutrino masses on black hole evaporation

“…Specifically, any charged black hole with mass less than approximately 10 5 M ⊙ will rapidly lose any initial electric charge [4,5]. Furthermore, unless there are a large number of undiscovered massless scalar fields in nature [6], black holes will quickly spin down, with their specific angular momentum a = J/M decreasing at roughly twice the rate their mass decreases [3].…”