Thermodynamics of Conformal Anomaly Corrected Black Holes in AdS Space

TL;DR

This paper derives exact solutions for conformal anomaly corrected black holes in AdS space and analyzes their thermodynamic stability and phase transitions, revealing novel behaviors depending on horizon curvature and anomaly coefficient.

Contribution

It provides the first analytical solutions for such black holes and explores their thermodynamic properties, including stability criteria and Hawking-Page transitions, influenced by the conformal anomaly.

Findings

Black holes with positive curvature horizons exhibit a minimal horizon size and Hawking-Page transition.

Ricci flat horizon black holes are always thermodynamically stable with no phase transition.

Negative curvature horizon black holes show a critical anomaly coefficient affecting stability and phase transitions.

Abstract

We present exact analytical black hole solutions with conformal anomaly in AdS space and discuss the thermodynamical properties of these black hole solutions. These black holes can have a positive, zero and negative constant curvature horizon, respectively. For the black hole with a positive constant curvature horizon, there exists a minimal horizon determined by the coefficient of the trace anomaly, the black hole with a smaller horizon is thermodynamically unstable, while it is stable for the case with a larger horizon. The Hawking-Page transition happens in this case. For the black hole with a Ricci flat horizon, the black hole is always thermodynamically stable and there is no Hawking-Page transition. In the case of the black hole with a negative constant curvature horizon, there exists a critical value for the coefficient of the trace anomaly, under this critical value, the black hole is always thermodynamical stable and the Hawking-Page transition does not happen. When the coefficient is beyond the critical value, the black hole with a smaller horizon is thermodynamically unstable, but it becomes stable for the case with a larger horizon, the Hawking-Page transition always happens in this case. The latter is a new feature for the black holes with a negative constant curvature horizon.