Thermodynamics and information recovery of Schwarzschild AdS black holes in conformal Killing gravity

TL;DR

This paper investigates Schwarzschild AdS black holes in conformal Killing gravity, analyzing their thermodynamics and information recovery, revealing how the conformal Killing gravity parameter influences phase transitions and the Page curve.

Contribution

It introduces the effects of conformal Killing gravity parameter on black hole thermodynamics, phase structure, and information recovery using the island formula.

Findings

Conformal Killing gravity parameter affects phase transitions and extremal limits.

Including islands restores the Page curve, ensuring unitarity.

Page time behavior depends on the gravity parameter and black hole size.

Abstract

We study Schwarzschild AdS black holes in conformal Killing gravity, focusing on their thermodynamics and information recovery via the island formula. Treating the cosmological constant as pressure and the conformal Killing gravity parameter as an independent variable, we find that the Bekenstein-Hawking area law holds, while the conformal Killing gravity parameter dramatically affects phase structure. For a positive conformal Killing gravity parameter, black holes admit an extremal limit and exhibit Van der Waals-like criticality with first and second order phase transitions; for a negative conformal Killing gravity parameter, no extremal limit or criticality occurs. Using the island prescription, we show that without islands, the entanglement entropy of Hawking radiation grows unboundedly, violating unitarity, while including islands after Page time restores the Page curve, with late-time entropy saturating at twice the Bekenstein-Hawking value. Page time can be expressed in terms of thermodynamic quantities, displaying critical behavior for positive conformal Killing gravity parameter, whereas in negative conformal Killing gravity small black holes recover information rapidly and large ones more slowly, with pressure reducing Page time. Our results reveal a direct link between black hole thermodynamics, quantum information recovery, and modified gravity.