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

Yahya Ladghami, Brahim Asfour, Francisco S. N. Lobo, Taoufik Ouali

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

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
Paper Structure (12 sections, 55 equations, 10 figures)

This paper contains 12 sections, 55 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Black Holes in Cotton Gravity
  3. Black Hole Solution
  4. Thermodynamics
  5. Positive Cotton Gravity
  6. Negative Cotton Gravity
  7. Island Formula
  8. Positive Cotton Gravity
  9. Negative Cotton Gravity
  10. Page Curve and Thermodynamic–Information Correspondence
  11. Evaporation Dynamics and Page Time Scaling
  12. Discussion and Conclusions

Figures (10)

  • Figure 1: Thermal evolution of Schwarzschild AdS black holes in Positive Cotton Gravity for different values of the pressure.
  • Figure 2: Gibbs free energy as a function of the Hawking temperature for different values of the pressure.
  • Figure 3: Heat capacity as a function of the event horizon radius for different values of the thermodynamic pressure.
  • Figure 4: Thermal evolution of Schwarzschild AdS black holes in negative Cotton gravity for different values of the thermodynamic pressure.
  • Figure 5: Gibbs free energy as a function of the Hawking temperature for $P=1$ and different values of the negative Cotton parameter.
  • ...and 5 more figures