Pair Creation of Black Holes During Inflation

TL;DR

This paper investigates the quantum pair creation of black holes during inflation, analyzing instantons, evolution, and the impact of quantum effects, and compares different wave function proposals for their physical plausibility.

Contribution

It introduces instantons for black hole pair creation during inflation, evaluates the no boundary proposal, and studies black hole evolution and magnetically charged black holes.

Findings

No boundary proposal yields physically sensible pair creation rates.

Most quantum-created black holes evaporate before inflation ends.

Magnetically charged black holes are exponentially rare in the current universe.

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.