Thermodynamics and information recovery of Schwarzschild AdS black holes in Cotton gravity

Abstract: We study Schwarzschild AdS black holes in Cotton gravity, focusing on their thermodynamics and information recovery via the island formula. Treating the cosmological constant as pressure and the Cotton parameter as an independent variable, we find that the Bekenstein-Hawking area law holds, while the Cotton parameter dramatically affects phase structure. For a positive Cotton parameter, black holes admit an extremal limit and exhibit Van der Waals-like criticality with first and second order phase transitions; for a negative Cotton 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 Cotton parameter, whereas in negative Cotton 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