Robert Mann D. Kubiznak, N. Altimirano, S. Gunasekaran, B. Dolan, D. Kastor, J. Traschen, Z. Sherkatgnad D.Kubiznak, R.B. Mann JHEP 1207 (2012) 033 S. Gunasekaran, D.Kubiznak, R.B. Mann JHEP 1211 (2012) 110 B. Dolan, D. Kastor, D.Kubiznak, R.B. Mann, J. Traschen Phys. Rev. D87 (2013) N. Altimirano, D.Kubiznak, R.B. Mann Phys. Rev. D88 (2013) N. Altimirano, D. Kubiznak, Z. Sherkatgnad, R.B. Mann CQG 31 (2014) N. Altimirano, D. Kubiznak, Z. Sherkatgnad, R.B. Mann Galaxies 2 (2014) 89 The Everyday Phenomena of Black Hole Chemistry

Black Hole Thermodynamics ThermodynamicsGravity

Smarr Formula Schwarzschild Black hole Schwarzschild-AdS Black hole Smarr L. Smarr PRL 30, 71 (1973) [Err. 30, 521 (1973)]. Smarr

Scaling Arguments Suppose S-AdS Black Hole Caldarelli/Cognola/Kl emm, CQG 17, 399 (2000)

Schwarzschild-AdS Black hole Smarr First Law Pressure from the Vacuum? Provided Thermodynamic Pressure Thermodynamic Volume Dolan CQG 28 (2011) ;

The Chemistry of AdS Black Holes Include gauge charges: First Law Smarr Relation Thermodynamic Potential: Gibbs Free Energy Equilibrium: Global minimum of Gibbs Free Energy Local Stability: Positivity of the Specific Heat

Mass as Enthalpy ThermodynamicsGravity Mass = Total Energy - Vacuum Contribution (infinite) Mass = Total Energy - Vacuum Contribution (infinite)

Everyday AdS Black Hole Thermodynamics Hawking Page Transition Van der Waals Fluid and Charged AdS Black Holes Reentrant Phase Transitions Black Hole Triple Points  Solid/Liquid/Gas

AF black holes evaporate by Hawking radiation AdS is like a confining box  static black holes in thermal equilibrium 1 st order transition between gas of particles and large black holes at Tc Hawking-Page Transition D-dim’l Schwarzschild-AdS Black hole S.W. Hawking & D.N. Page Comm Math. Phys. 87 (1983) 577

Phase transition in dual CFT (quark-gluon plasma) Fluid interpretation: solid/liquid PT (infinite coexistence line) Planar black holes  ideal gas Equation of state depends on the horizon topology Witten (1998) D. Kubiznak/RBM arXiv [ ]

Van der Waals Fluids Critical Point law of correspondin g states

PV Diagram for a VdW Fluid Maxwell’s Equal Area Law

First Law Gibbs Free Energy characteristic of the gas

Clausius-Clapeyron equation Line of Coexistence Critical Exponents For a VdW Fluid Specific Heat Order Parameter Isothermal Compressibility Critical Isotherm

Charged AdS Black Holes as Van der Waals Fluids Temperature Entropy Potential Pressure Volume Smarr RelationFirst Law Kubiznak/Mann JHEP 1207 (2012) 033

Equation of State Physical Equation of State Thermodynamic Volume Van der Waal’s Equation

Gibbs Free Energy of AdS RN BH Just like a VdW Fluid! Fixed Charge NB: Disagree with Chamblin et.al. PRDD60 (1999) ;

Critical Behaviour Just like a VdW Fluid! law of correspondin g states

Just like a VdW Fluid! govern volume, compressibility, specific heat, and pressure near the critical point

RPT: If a monotonic variation of any thermodynamic quantity that results in two (or more) phase transitions such that the final state is macroscopically similar to the initial state. Reentrant Phase Transitions T. Narayanan and A. Kumar Physics Reports 249 (1994) 135 multicomponent fluid systems gels ferroelectrics liquid crystals binary gases First observed in nicotine/water C. Hudson Z. Phys. Chem. 47 (1904) 113.

Single-Rotation Black Holes Smarr RelationFirst Law

Dimensional Dependence of G Zeroth-Order Phase Transition

Reentrant Phase Transitions in D>5 Zeroth-Order Phase Transition

Reentrant Phase Transitions in D>5 Coexistence Lines

NO BLACK HOLES

Slow and Ultraspinning Limits

RPTs do not require variable cosmological constant J/T Phase Diagram N. Altimirano, D. Kubiznak, Z. Sherkatgnad, R.B. Mann Galaxies 2 (2014) 89

Triple Points in Multiply Rotating Black Holes Triple Point! N. Altimirano, D. Kubiznak, Z. Sherkatgnad, R.B. Mann CQG 31 (2104) arXiV:

Reentrant Phase transition Ending in a Triple Point

N. Altimirano, D. Kubiznak, Z. Sherkatgnad, R.B. Mann CQG 31 (2014) The Black Hole Triple Point

Continuous variation of N is probably OK. Classical gravity corresponds to (similar to TD limit…can vary number of moles continuously) Quantized N…quantum gravity effects? “Grand-canonical ensemble of stringy vacua” with conjugate quantity playing role of “chemical potential”? Variable and AdS/CFT?

Summary Cosmological Pressure can be understood as a Thermodynamic Quantity – First Law is modified to include a pressure-volume term Smarr Law needs to be modified to respect scaling Mass becomes Enthalpy “Everyday Chemical Thermodynamics” is manifest – Van der Waals Transitions Small/large  liquid/gas phase Critical Phenomena analogous – Reentrant Phase Transitions – Triple Points These phenomena do not require a variable cosmological constant!

Open Questions Meaning of Conjugate Volume? Compressibility and Stability? Gauge/Gravity Duality interpretation? More exotic black holes? – Lovelock Black Holes? – Lifshitz Black Holes? 1+1 Pressure-Volume? Meaning of de Sitter Thermodynamics? Other “everyday analogues”? D. Kubiznak, N. Altimirano, W. Brenna, M. Park, F. Simovic, Z. Sherkatgnad, J. Mureika, S. Solodukhin Mo/Li/Liu; Wei/Liu; Ballik/Lake Dutta/Jain/Soni; Zhou/Zhang/Wang Breton/Vergliaffa; Cai/Cao/Zhang; Allahverdizadeh/Lemos/Sheykhi; Lu/Pang/Pope/Vasquez-Portiz