Evaporation of Primordial Charged Black Holes: Timescale and Evolution of Thermodynamic Parameters

Abstract

The evolution of primordial black holes formed during the reheating phase is revisited. For reheating temperatures in the range of 1012–1013 GeV, the initial masses are respectively of the order of 1010–108MP, where MP is the Planck mass. These newborn black holes have a small charge-to-mass ratio of the order of 10−3, a consequence of statistical fluctuations present in the plasma constituting the collapsing matter. Charged black holes can be rapidly discharged by the Schwinger mechanism, but one expects that, for very light black holes satisfying the condition M/MP<<MP/mW (mW is the mass of the heaviest standard model charged W-boson), the pair production process is probably strongly quenched. Under these conditions, these black holes evaporate until attaining extremality with final masses of about 107–105MP. Timescales to reach extremality as a function of the initial charge excess were computed, as well as the evolution of the horizon temperature and the charge-to-mass ratio. The behavior of the horizon temperature can be understood in terms of the well-known discontinuity present in the heat capacity for a critical charge-to-mass ratio Q/GM=3/2.