Primordial Black Holes: Pair Creation, Lorentzian Condition, and Evaporation

Abstract

The wave function of the universe is usuallytaken to be a functional of the threemetric on aspacelike section, Σ, which is measured. It issometimes better, however, to work in the conjugaterepresentation, where the wave function depends on a quantityrelated to the second fundamental form of Σ. Thismakes it possible to ensure that Σ is part of aLorentzian universe by requiring that the argument of the wave function be purely imaginary. Wedemonstrate the advantages of this formalism first inthe well-known examples of the nucleation of a de Sitteror a Nariai universe. We then use it to calculate the pair creation rate for submaximal blackholes in de Sitter space, which had been thought tovanish semiclassically. We also study the quantumevolution of asymptotically de Sitter black holes. Forblack holes whose size is comparable to that of thecosmological horizon, this process differs significantlyfrom the evaporation of asymptotically flat black holes.Our model includes the one-loop effective action in the s-wave and large-N approximation.Black holes of the maximal mass are in equilibrium.Unexpectedly, we find that nearly maximal quantumSchwarzschild–de Sitter black holes antievaporate.However, there is a different perturbative mode thatleads to evaporation. We show that this mode will alwaysbe excited when a pair of maximal cosmological blackholes nucleates.