Mass and Thermodynamic Volume in Lifshitz Spacetimes

Abstract

We examine the concept of black hole thermodynamic volume and its consistency with thermodynamic mass in spacetimes that are not asymptotically flat but instead have anisotropic Lifshitz scaling symmetry. We find that the generalized Smarr relation in anti de Sitter space -- extended to include a pressure-volume term -- holds here as well, and that there exists a definition of thermodynamic mass and thermodynamic volume that satisfy both this relation and the $1^{st}$ law of thermodynamics. We compare the thermodynamic mass with other known quantities such as ADM, Brown-York and Hollands-Ishibashi-Marolf masses. We also conjecture methods for obtaining a thermodynamic mass where there is ambiguity due to the cosmological constant lengthscale depending on the horizon radius lengthscale.

19 pages, 4 figures, REVTex 4; with additional corrections

References in corpus (15)

• Black Hole Enthalpy and an Entropy Inequality for the Thermodynamic Volume
• Multiple Reentrant Phase Transitions and Triple Points in Lovelock Thermodynamics
• Black holes in asymptotically Lifshitz spacetime
• AdS and Lifshitz Black Holes in Conformal and Einstein-Weyl Gravities
• Quasilocal mass in general relativity
• Signature of the Van der Waals like small-large charged AdS black hole phase transition in quasinormal modes
• Critical behavior of charged Gauss-Bonnet AdS black holes in the grand canonical ensemble
• Pathologies in Asymptotically Lifshitz Spacetimes
• Ehrenfest scheme for $P-V$ criticality of higher dimensional charged black holes, rotating black holes and Gauss-Bonnet AdS black holes
• Thermodynamics of phase transition in higher dimensional Reissner-Nordström-de Sitter black hole
• A unified phase transition picture of the charged topological black hole in Horava-Lifshitz gravity
• Thermodynamics of Lifshitz Black Holes
• Continuous phase transition and critical behaviors of 3D black hole with torsion
• Nonlinearly charged Lifshitz black holes for any exponent $z>1$
• Conserved Killing charges of quadratic curvature gravity theories in arbitrary backgrounds

Cited by in corpus (45)

• Black hole chemistry: thermodynamics with Lambda
• Noether charge, black hole volume, and complexity
• Lifshitz holography
• Holographic Thermodynamics Requires a Chemical Potential for Color
• Holographic Thermodynamics of Accelerating Black Holes
• Black holes in Einsteinian cubic gravity
• Heat Engines for Dilatonic Born-Infeld Black Holes
• Combined effects of f(R) gravity and conformally invariant Maxwell field on the extended phase space thermodynamics of higher-dimensional black holes
• Hyperscaling violating black holes with spherical and hyperbolic horizons
• Effects of power-law Maxwell field on the Van der Waals like phase transition of higher dimensional dilaton black holes
• Black hole thermodynamics and heat engines in conformal gravity
• Holographic entanglement chemistry
• Thermodynamic properties of higher-dimensional dS black holes in dRGT massive gravity
• Black Hole Enthalpy and Scalar Fields
• Extracting energy via magnetic reconnection from Kerr-de Sitter black holes
• Black Hole Chemistry: the first 15 years
• Critical behavior of charged AdS black holes surrounded by quintessence via an alternative phase space
• Thermodynamic Instabilities of Generalized Exotic BTZ Black Holes
• Microscopic entropy of higher-dimensional nonminimally dressed Lifshitz black holes
• Maxwell's equal area law for Lovelock Thermodynamics
• The correspondence between thermodynamic curvature and isoperimetric theorem from ultraspinning black hole
• Critical behaviour of Lifshitz dilaton black holes
• Phase transition and entropic force of de Sitter black hole in massive gravity
• Thermodynamic Volume and the Extended Smarr Relation
• Super-entropic black hole with Immirzi hair
• Cardy formula for charged black holes with anisotropic scaling
• Hyperscaling violating black holes in scalar-torsion theories
• Ricci cubic gravity in d dimensions, gravitons and SAdS/Lifshitz black holes
• Regular BTZ black holes from an infinite tower of corrections
• Holography without counter terms
• Thermodynamic Volume of Cosmological Solitons
• Thermodynamics of $z=4$ Hořava-Lifshitz black holes
• Scalar fields and Lifshitz black holes from Derrick's theorem evasion
• BTZ black hole with KdV-type boundary conditions: Thermodynamics revisited
• Entropy of higher-dimensional charged de Sitter black holes and phase transition
• Complexity Growth, Butterfly Velocity and Black hole Thermodynamics
• Thermodynamic Instability of $3D$ Einstein-Born-Infeld AdS Black Holes
• Entropy of higher-dimensional topological dS black holes with nonlinear source
• Black hole solutions to Einstein-Bel-Robinson gravity
• Charged Lifshitz black hole and probed Lorentz-violation fermions from holography
• Super-entropic black holes in gravity's rainbow and determining constraints on rainbow functions
• Thermodynamic Properties of Kehagias-Sfetsos Black Hole \& KS/CFT Correspondence
• Area products for ${\mathcal{H}}^{\pm }$ in AdS space
• Holographic stress tensor of colored Lifshitz spacetimes and hairy black holes
• Generalized Thermodynamic Properties of Lifshitz black holes