Pair Creation of Black Holes During Inflation
Raphael Bousso, Stephen W. Hawking
TL;DR
The paper analyzes black hole pair creation during inflation using gravitational instantons within the Hartle-Hawking no boundary framework, contrasting with the tunnelling proposal.Neutral BHs are produced with a rate $\\Gamma = \exp(-\\pi/\\Lambda_{\\rm eff}(\\phi_0))$, implying abundant Planck-scale holes early and strong suppression for larger ones, while magnetically charged BHs are far rarer in Einstein–Maxwell theory.Classical evolution shows horizons grow due to energy flux from the rolling inflaton, but quantum effects generally cause neutral BHs to evaporate before inflation ends, whereas charged BHs can survive only under special conditions or alternative theories such as dilatons.Overall, the no boundary approach provides a consistent quantum cosmological picture of primordial BH formation during inflation and imposes constraints on early-universe models and potential extensions.
Abstract
Black holes came into existence together with the universe through the quantum process of pair creation in the inflationary era. We present the instantons responsible for this process and calculate the pair creation rate from the no boundary proposal for the wave function of the universe. We find that this proposal leads to physically sensible results, which fit in with other descriptions of pair creation, while the tunnelling proposal makes unphysical predictions. We then describe how the pair created black holes evolve during inflation. In the classical solution, they grow with the horizon scale during the slow roll-down of the inflaton field; this is shown to correspond to the flux of field energy across the horizon according to the First Law of black hole mechanics. When quantum effects are taken into account, however, it is found that most black holes evaporate before the end of inflation. Finally, we consider the pair creation of magnetically charged black holes, which cannot evaporate. In standard Einstein-Maxwell theory we find that their number in the presently observable universe is exponentially small. We speculate how this conclusion may change if dilatonic theories are applied.