Evaporation of a Kerr black hole by emission of scalar and higher spin particles

Abstract

We study the evolution of an evaporating rotating black hole, described by the Kerr metric, which is emitting either solely massless scalar particles or a mixture of massless scalar and nonzero spin particles. Allowing the hole to radiate scalar particles increases the mass loss rate and decreases the angular momentum loss rate relative to a black hole which is radiating nonzero spin particles. The presence of scalar radiation can cause the evaporating hole to asymptotically approach a state which is described by a nonzero value of ${a}_{*}\ensuremath{\equiv}a/M.$ This is contrary to the conventional view of black hole evaporation, wherein all black holes spin down more rapidly than they lose mass. A hole emitting solely scalar radiation will approach a final asymptotic state described by ${a}_{*}\ensuremath{\simeq}0.555.$ A black hole that is emitting scalar particles and a canonical set of nonzero spin particles (3 species of neutrinos, a single photon species, and a single graviton species) will asymptotically approach a nonzero value of ${a}_{*}$ only if there are at least 32 massless scalar fields. We also calculate the lifetime of a primordial black hole that formed with a value of the rotation parameter ${a}_{*},$ the minimum initial mass of a primordial black hole that is seen today with a rotation parameter ${a}_{*},$ and the entropy of a black hole that is emitting scalar or higher spin particles.