Hawking radiation inside a rotating black hole

TL;DR

This paper investigates Hawking radiation perception by various freely falling observers inside and outside a rotating Kerr black hole, revealing observer-dependent effects and temperature divergences near the inner horizon.

Contribution

It generalizes the analysis of Hawking radiation to different observer classes within Kerr black holes, including inside the event horizon, and examines the temperature behavior at the horizons.

Findings

Effective temperature remains regular at the event horizon.

Temperature becomes negative and diverges at the Cauchy horizon.

Hawking spectrum is a graybody decreasing with black hole spin.

Abstract

In semiclassical gravity, the vacuum expectation value ${\langle\hat{N}\rangle}$ of the particle number operator for a quantum field gives rise to the perception of thermal radiation in the vicinity of a black hole. This Hawking effect has been examined only for observers asymptotically far from a Kerr black hole; here we generalize the analysis to various classes of freely falling observers both outside and inside the Kerr event horizon. Of note, we find that the effective temperature of the ${\langle\hat{N}\rangle}$ distribution remains regular for observers at the event horizon but becomes negative and divergent for observers reaching the inner Cauchy horizon. Furthermore, the perception of Hawking radiation varies greatly for different classes of observers, though the spectrum is generally a graybody that decreases in intensity with black hole spin and increases in temperature when looking toward the edges of the black hole shadow.