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Thermodynamics and Phase Transition of Black Hole in High-dimensional Massive Gravity

This study explores reentrant phase transitions of higher-dimensional AdS black holes, water-like phase transitions, and Van der Waals-like phase behavior in charged AdS black holes. It also discusses topological black holes in Born-Infeld-Massive Gravity and critical phenomena. The research examines the extended phase space of black holes and their thermodynamic properties, providing insights into the behavior of quasinormal modes and the cosmological implications of massive gravity theories. Various critical points, including triple points and isothermal phase transitions, are analyzed in detail.

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Thermodynamics and Phase Transition of Black Hole in High-dimensional Massive Gravity

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  1. Thermodynamics and phase transition of Black hole in high dimensional massive gravity Ruihong Yue Centerfor Gravity and Cosmology, Yangzhou University 5th Dark Matter Dark Energy and Matter-Antimatter Asymmetry， 2018.12.29atFoGuangshan 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. 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. 1. Model and solution: Part B. Reentrant phase trans. AdS bh in dRGT massive gravity Λ: cosmological constant, m the mass Consider a spherical symmetric solution: EPJC77:256, DOI 10.1140/epjc/s10052-017-4822-9

  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

  13. 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

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

  15. equation of state: Determining the critical point

  16. P-r picture with different temperatures

  17. G-T picture with different pressures

  18. P-T phase transition picture

  19. Case 2

  20. 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

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

  22. 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

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

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

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

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

  27. 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

  28. Theaction of BIMG Advance in High energy Physics (2017) 3819246 di=d-i

  29. Thethermodynamic quantities

  30. 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.

  31. Thank you for your attention!

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

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

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