Quantum Gravity Effects in the Kerr Spacetime

TL;DR

This paper investigates how quantum gravity effects modify the structure and thermodynamics of rotating black holes using a renormalization group approach within Quantum Einstein Gravity, revealing significant deviations from classical predictions.

Contribution

It introduces a novel renormalization group improvement of the Kerr metric in QEG, analyzing quantum corrections to horizons, ergosphere, and thermodynamics of rotating black holes.

Findings

Quantum corrections alter the horizon and ergosphere structure.

The Smarr formula remains classical despite quantum effects.

The black hole temperature deviates from the classical surface gravity relation.

Abstract

We analyze the impact of the leading quantum gravity effects on the properties of black holes with nonzero angular momentum by performing a suitable renormalization group improvement of the classical Kerr metric within Quantum Einstein Gravity (QEG). In particular we explore the structure of the horizons, the ergosphere, and the static limit surfaces as well as the phase space avilable for the Penrose process. The positivity properties of the effective vacuum energy momentum tensor are also discussed and the "dressing" of the black hole's mass and angular momentum are investigated by computing the corresponding Komar integrals. The pertinent Smarr formula turns out to retain its classical form. As for their thermodynamical properties, a modified first law of black hole thermodynamics is found to be satisfied by the improved black holes (to second order in the angular momentum); the corresponding Bekenstein-Hawking temperature is not proportional to the surface gravity.