P-V criticality in the extended space of black holes

1. P-V criticality in the extended space of black holes Speaker：Ya-Peng Hu （胡亚鹏） College of Science, Nanjing University of Aeronautics and Astronautics （南京航空航天大学理学院） 2019.10.15 @Fragrant Hill, Beijing International Joint Workshop on the standard Model and beyond

2. A. Introduction 1) Stationary black hole and its four laws of thermodynamics 2) P-V criticality in the extended space of Reissner– Nordstrom-AdS black hole: another analogy 3) Some motivations of further investigations on P-V criticality B. P-V criticality in the extended space of black holes in massive gravity C. P-V criticality in the extended space of black holes in Horndeski gravity D. Conclusion and discussion

3. A. Introduction 1) Stationary black hole and its four laws of thermodynamics • Area & entropy: Horizon area A increase; Hawking area theorem; Bekenstein proposal • Kerr-Newman black hole: similar with the first law of thermodynamics of rotating celestial body Mass & internal energy, surface gravity & temperature, Area & entropy

4. Four laws of black hole mechanics by Bardeen、Carter and Hawking • Comparisons with four laws of thermodynamics

5. Hawking radiation: • Bekenstein-Hawking entropy: Notes: i) Stationary black holes, dynamical? ii) Micro states of a black hole? iii) Key insights on essence of gravity: AdS/CFT, information paradox, emergent gravity, …… iv) Analogies of other thermodynamics phenomena in gravity? For example, phase transition……

6. 2) P-V criticality in the extended space of Reissner– Nordstrom-AdS black hole: another analogy • Van der Waals gas-liquid phase transition and criticality:

7. P-V phase diagram of Van der Waals gas and its criticality: Critical exponents and scaling laws:

8. P-V criticality in Reissner-Nordstrom-AdS black hole Action: Solution: Horizon: Temperature: Key point 1: Pressure

9. Key point 2: Equation of state and specific volume for RN-AdS black hole P-V criticality in RN-AdS black hole:

10. Same Critical exponents:

11. 3) Some motivations of further investigations on P-V criticality • P-V criticality in other AdS black holes in modified gravity?---Many works • Further physical understanding of this P-V criticality? For example, pressure deduced at microscopic level? • Charged, horizon with spherical topology k=1, pressure related to cosmological constant? • Some potential insights into essence of gravity?

12. B. P-V criticality in the extended space of black holes in massive gravity 1)dRGT massive gravity • ghost free: Hassan and Rosen, 2012 (de Rham, Gabazaze, and Tolley, 2012)

13. 2) Black hole solutions and their thermodynamics • Black hole solutions N(r)=1

14. Thermodynamics

15. 3) P-V criticality in the extended space of four-dimensional black holes in massive gravity • Pressure: • State equation: • Critical point:

16. Critical exponents: Key notes in massive gravity cases： P-V criticality also exist in k=0, -1 cases

17. C. P-V criticality in the extended space of black holes in Horndeski gravity 1) Horndeski gravity with a non-minimal kinetic coupling: • Black hole solutions:

18. Thermodynamics of this black hole: • First law of black hole thermodynamics in extended phase space: • Main state equations:

19. 3) P-V criticality in the extended space of black holes in Horndeski gravity: First case • Pressure and state equation: • P-V diagram: Key result: No criticality in this case

20. 4) P-V criticality in the extended space of this black hole: New cases • Asymptotical behavior: effective AdS radius • More reasonable pressure defined: • State equation:

21. For zero cosmological constant: • For negative cosmological constant: Main results: i) Should choose ‘+’ branch; ii) Exists P-V criticality; iii) Not all parameters region;

22. Critical point and exponents: Numerical

23. For positive cosmological constant: Main results: i) Both branches can be chosen; ii) ‘+’ branch exists P-V criticality; iii) ‘-’ branch does not exist P-V criticality; iv) Not all parameters region;

24. P-V diagrams for two branches: Critical point and exponents: Numerical

25. Key notes in Horndeski gravity cases (Y.P Hu et al, Phys.Rev.D100, 084004,2019)： i) Introduce amore reasonable pressure instead of the previous pressure ii) Obtain P-V criticality in the two cases with zero and positive cosmological constant for the first time; iii) Imply that the cosmological constant Λ may not be a necessary pressure candidate for black holes at the microscopic level;

26. C. Conclusion and discussion • Conclusion: 1) A brief introduction on background and motivations of P-V criticality in AdS black holes; 2) P-V criticality without charge: Gauss-Bonnet cases; 3) P-V criticality with k=0, -1 horizon topology: massive gravity cases; 4) P-V criticality with zero or positive cosmological constant: Horndeski gravity cases;

27. Discussion: 1) Is Asymptotical AdS behavior necessary? 2) Further physical understanding on this P-V criticality and phase transition; 3) Duality from AdS/CFT; 4) Beyond the mean field theory; 5) Renormalization group in black holes; 6) Potential insights on essence of gravity; Beyond the GR……?

28. Thanks!