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

Abstract

Static black holes in the conformal anomaly-sourced semiclassical general relativity in four dimensions were recently extended to rotating, stationary solutions. 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 α of the A-type trace anomaly is nonzero, we show that: (i) the cosmological constant is bounded from above, i.e., Λ ≤ 3/4 α; (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 for black holes are problematic.