Hawking radiation from extremal and non-extremal black holes

TL;DR

This paper analyzes the relationship between Hawking radiation in extremal and non-extremal Reissner-Nordstrom black holes, showing that regular collapsing geometries connect their stress energy tensors smoothly, with late time transients crucial for extremal cases.

Contribution

It demonstrates that the stress energy tensor remains regular in the extremal limit and emphasizes the importance of late time transients, challenging previous assumptions about singularities.

Findings

Stress energy tensor remains regular in extremal limit

Late time transients are essential for extremal black holes

Singular behavior arises from neglecting transients in late time limit

Abstract

The relationship between Hawking radiation emitted by non extremal and extremal Reissner Nordstrom black holes is critically analyzed. A careful study of a series of regular collapsing geometries reveals that the stress energy tensor stays regular in the extremal limit and is smoothly connected to that of non extremal black holes. The unexpected feature is that the late time transients which played little role in the non extremal case are necessary to preserve the well defined character of the flux in the extremal case. The known singular behavior of the static energy density of extremal black holes is recovered from our series by neglecting these transients, when performing what turns out to be an illegitimate late time limit. Although our results are derived in two dimensional settings, we explain why they should also apply to higher dimensional black holes.