Kerr-Vaidya type radiating black holes in semi-classical gravity with conformal anomaly

TL;DR

This paper derives radiating Kerr-Vaidya-type black hole solutions in semi-classical gravity with conformal anomaly, revealing constraints on the cosmological constant and issues with black hole thermodynamics and stability.

Contribution

It extends previous static and stationary black hole solutions to non-stationary, radiating cases in semi-classical gravity with conformal anomaly, highlighting new physical constraints and thermodynamic challenges.

Findings

Cosmological constant is bounded by the anomaly coupling constant.

Static black holes may not be unique and violate the second law.

Non-stationary solutions face stability and thermodynamic issues.

Abstract

Static black holes in the conformal anomaly-sourced semi-classical General Relativity in four dimensions were extended to rotating, stationary solutions, recently. These quantum-corrected black holes show different features compared to the Kerr black hole and need for further extensions. Here we remove the condition of stationarity and find radiating (Kerr-Vaidya-type) solutions in the same theory augmented with a cosmological constant. As long as the coupling constant $\alpha$ of the $A$-type trace anomaly is non-zero, we show that $i)$ the cosmological constant is bounded from above, i.e $\Lambda \le \frac{3}{4 \alpha}$; $ii)$ static black holes exist but they may not be unique; $iii)$ static black holes do not satisfy the second law of black hole thermodynamics; $iv)$ static black holes may have unstable inner horizons; $v)$ In the nonstationary and axially symmetric case, stability of the event horizon and the second law of thermodynamics black holes are problematic.