Quantum black hole inflation

TL;DR

This paper proposes a new approach to particle creation in strong gravitational fields, deriving conditions for real particle production near black holes and suggesting a model for eternal inflation starting from a Planck-scale black hole.

Contribution

It introduces a novel method based on the Heisenberg uncertainty principle to analyze particle creation and derives a natural power law for black hole horizon development and area spectrum.

Findings

Derived an upper limit for particle creation region outside black hole horizons.

Established a power law for the development of the event horizon.

Proposed a cosmological model leading to eternal inflation from a Planck-scale black hole.

Abstract

In this paper we follow a new approach for particle creation by a localized strong gravitational field. The approach is based on a definition of the physical vacuum drawn from Heisenberg uncertainty principle. Using the fact that the gravitational field red-shifts the frequency modes of the vacuum, a condition on the minimum stregth of the gravitational field required to achieve real particle creation is derived. Application of this requirement on a Schwartzchid black hole resulted in deducing an upper limit on the region, outside the event horizon, where real particles can be created. Using this regional upper limit, and considering particle creation by black holes as a consequence of the Casimir effect, with the assumption that the created quanta are to be added to the initial energy, we deduce a natural power law for the development of the event horizon, and consequently a logarithmic law for the area spectrum of an inflating black hole. Application of the results on a cosmological model shows that if we start with a Planck-dimensional black hole, then through the process of particle creation we end up with a universe having the presently estimated critical density. Such a universe will be in a state of eternal inflation.