Hawking radiation at the zero temperature limit

TL;DR

This paper extends Hawking radiation to zero temperature Kerr black holes, showing continued emission for certain modes and deriving explicit absorption probabilities, with implications for black hole extremality and cosmic censorship.

Contribution

It demonstrates that Kerr black holes can radiate at zero temperature for specific modes and provides explicit formulas for absorption probabilities, advancing understanding of black hole thermodynamics.

Findings

Radiation ceases for modes with  > m  as surface gravity vanishes.

Black holes continue to radiate for  < m  at T=0.

Emission rate peaks at =(m)/2 for both bosonic and fermionic modes.

Abstract

We show that the thermal radiation derived by Hawking can be smoothly extended to the $T=0$ limit for Kerr black holes. The emission of the modes with $\omega > m\Omega $ comes to a halt as the surface gravity vanishes. However, Kerr black holes smoothly continue to radiate both in bosonic and fermionic modes with $\omega < m\Omega$, at the $T=0$ limit. We derive explicit expressions for the absorption probabilities which imply that the highest rate of emission pertains to the modes with $\omega=(m\Omega)/2$, both for bosonic and fermionic cases. At the zero limit of thermal radiation, the number of emitted particles vanishes as $\omega \to 0$, which strictly differentiates it from the non-thermal radiation of soft particles by extremal Kerr black holes. We also note that the thermal radiation at the zero limit, drives the black hole away from extremality in accord with the third law and the cosmic censorship conjecture