Late-time particle creation from gravitational collapse to an extremal Reissner-Nordstrom black hole

TL;DR

This paper demonstrates that extremal Reissner-Nordstrom black holes do not emit particles at late times, confirming the traditional belief through explicit calculations of particle flux and stress-energy tensor decay.

Contribution

It provides explicit calculations showing the decay of particle creation and stress-energy tensor in extremal RN black holes, confirming they do not emit particles at late times.

Findings

Particle flux approaches zero faster than any inverse power of time.

Stress-energy tensor expectation value drops to zero at late times.

Supports the belief that extremal black holes do not emit particles.

Abstract

We investigate the late time behavior of particle creation from an extremal Reissner-Nordstrom (RN) black hole formed by gravitational collapse. We calculate explicitly the particle flux associated with a massless scalar field at late times after the collapse. Our result shows that the expected number of particles in any wave packet spontaneously created from the ``in'' vacuum state approaches zero faster than any inverse power of time. This result confirms the traditional belief that extremal black holes do not emit particles. We also calculate the expectation value of the stress energy tensor in a 1+1 RN black hole and show that it also drops to zero at late times. Some comments on previous work by other authors are provided.