1. Thermodynamics and phase transition of Black hole in high dimensional massive gravity
Ruihong Yue
Center for Gravity and Cosmology, Yangzhou University
5th Dark Matter Dark Energy and Matter-Antimatter Asymmetry， at FoGuangshan
Collaborater:
Decheng Zou, Yunqi Liu, Zhanying Yang
Dr.s Ming Zhang, Bo Liu

2. Outline Part A: Introduction
Part B : Reentrant phase transitions of higher-dimensional AdS black holes in dRGT massive gravity
Part C: Water-like Phase Transitions and Triple Points of higher-dimensional Ads-BH in dRGT
Part D: Behavior of quasinormal modes and Van derWaals-like phase transition of charged AdS black holes in massive gravity
Part E：Reentrant Phase Transitions and Triple Points of Topological AdS Black Holes in Born-Infeld-Massive Gravity
Part F: Disscussion

3. 2. Accelerated expansion of universe: cosmological constant
Part A: Introduction
Einstein: spin-2, massless
Possible extension
2. Accelerated expansion of universe:
cosmological constant
dark matter dark energy
3. Massive gravity possibly provides an explanation for late-time acceleration

4. 1. Fierz and Pauli：linear theory
Dam，Veltman，Zakharov discontinuity
Nonlinear theory：Boulware-Deser ghost
2. De Rham-Gabadadze-Tolley.
spherically symmetric BH solution, charged BH, black string solution, BTZ-like BH
3. Thermodynamics Ads BH has been generalized into the extended phase space by treating cosmologic constant as the pressure of BH.

5. Outline
Part A: Introduction
Part B : Reentrant phase transitions of higher-dimensional AdS black holes in dRGT massive gravity
Part C: Water-like Phase Transitions and Triple Points of higher-dimensional Ads-BH in dRGT
Part D: Behavior of quasinormal modes and Van derWaals-like phase transition of charged AdS black holes in massive gravity
Part E：Reentrant Phase Transitions and Triple Points of Topological AdS Black Holes in Born-Infeld-Massive Gravity
Part F: Disscussion

6. Λ: cosmological constant, m the mass
Part B. Reentrant phase trans. AdS bh in dRGT massive gravity
1. Model and solution:
Λ: cosmological constant, m the mass
Consider a spherical symmetric solution:
EPJC77:256,
DOI /epjc/s

7. Final sol.
Using the definition the horizon of BH, f(r+)=0, one can find the mass, entropy and temperature of BH to be

8. 2. Critical Behavior of d-dim. Ads BH equation of state:
Determine the critical point

9. d>5
Gibbs free
energy：

10. P-r figure with w2=-1,w3=1：

11. G-T figure with w2=-1,w3=1,w4=-0.7

12. P-T figure with w2=-1,w3=1,w4=-0.7

14. Outline
Part A: Introduction
Part B : Reentrant phase transitions of higher-dimensional AdS black holes in dRGT massive gravity
Part C: Water-like Phase Transitions and Triple Points of higher-dimensional Ads-BH in dRGT
Part D: Behavior of quasinormal modes and Van derWaals-like phase transition of charged AdS black holes in massive gravity
Part E：Reentrant Phase Transitions and Triple Points of Topological AdS Black Holes in Born-Infeld-Massive Gravity
PartF: Disscussion

15. 1. Model and solution: BH sol. arxiv1810.07885
Part C. Water-like Phase Transitions and Triple Points in dRGT
1. Model and solution: N
BH sol.
arxiv

17. Determining the critical point
equation of state:
Determining the critical point

18. P-r picture with different temperatures

19. G-T picture with
different pressures

20. P-T phase transition picture

21. Case 2

22. Outline
Part A: Introduction
Part B : Reentrant phase transitions of higher-dimensional AdS black holes in dRGT massive gravity
Part C: Water-like Phase Transitions and Triple Points of higher-dimensional Ads-BH in dRGT
Part D: Behavior of quasi-normal modes and Van der Waals-like phase transition of charged AdS black holes in massive gravity
Part E：Reentrant Phase Transitions and Triple Points of Topological AdS Black Holes in Born-Infeld-Massive Gravity
Part F: Disscussion

23. Part D: Behavior of quasinormal modes of charged AdS BH
EPJC（2017）77:365

24. 1.Perturbation of charged Ads-BH in massive gravity by massless scalar field satisfying
Decomposing Psi in terms of radial function phi and harmonic function Ylm and an time oscillating factor

25. A:Isobaric phase trans. ( P fixed <Pc)
q=2,m=1,
c1=0.05,c2=2
Arrow indicates
the increase of BH
horizon radius

26. A: Isobar phase trans. ( P fixed=pc)
B: Isothermal phase trans. ( T fixed<Tc)

27. B: Isothermal phase trans. ( T fixed<Tc)

28. B:Isothermal phase trans. ( T fixed, T=Tc)

29. Outline
Part A: Introduction
Part B : Reentrant phase transitions of higher-dimensional AdS black holes in dRGT massive gravity
Part C: Water-like Phase Transitions and Triple Points of higher-dimensional Ads-BH in dRGT
Part D: Behavior of quasinormal modes and Van derWaals-like phase transition of charged AdS black holes in massive gravity
Part E：Reentrant Phase Transitions and Triple Points of Topological AdS Black Holes in Born-Infeld-Massive Gravity
Part F: Disscussion

30. The action of BIMG di=d-i
Advance in High energy Physics (2017)
di=d-i

31. The thermodynamic quantities

36. 3. There are Van der Waals SBH/LBH and RPT SBH/IBH in BI-dRGT.
Discussion:
1.There are Van der Waals SBH/LBH and RPT SBH/IBH in dRGT.
2.The quasi-normal modes behave differently in SBH and LBH regions, indicating the PT of charged AdsBH in dRGT.
3. There are Van der Waals SBH/LBH and RPT SBH/IBH in BI-dRGT.
4. There are Water-like SBH/LBH , SBH/IBH and IBH/LBH in dRGT.
5. Expecting the rich structure of PT in N-dimension gravity with multi-parameters.

37. Thank you for your attention!

38. The spherical BH in 5D GB and perturbation of scaler field

39. A: Isobar phase trans. ( P fixed<pc)