Misner-Sharp Mass and the Unified First Law in Massive Gravity

Abstract

We obtain the Misner-Sharp mass in the massive gravity for a four dimensional spacetime with a two dimensional maximally symmetric subspace via the inverse unified first law method. Significantly, the stress energy is conserved in this case with a widely used reference metric. Based on this property we confirm the derived Misner-Sharp mass by the conserved charge method. We find that the existence of the Misner-sharp mass in this case does not lead to extra constraint for the massive gravity, which is notable in modified gravities. In addition, as a special case, we also investigate the Misner-Sharp mass in the static spacetime. Especially, we take the FRW universe into account for investigating the thermodynamics of the massive gravity. The result shows that the massive gravity can be in thermodynamic equilibrium, which fills in the gap in the previous studies of thermodynamics in the massive gravity.

11 pages, no figure, version published in PRD

References in corpus (38)

• Resummation of Massive Gravity
• Massive Gravity
• Thermodynamic Behavior of Friedmann Equation at Apparent Horizon of FRW Universe
• Unified First Law and Thermodynamics of Apparent Horizon in FRW Universe
• Friedmann Equations of FRW Universe in Scalar-tensor Gravity, f(R) Gravity and First Law of Thermodynamics
• Thermodynamic route to Field equations in Lanczos-Lovelock Gravity
• Hawking Radiation of Apparent Horizon in a FRW Universe
• Thermodynamics of Black Holes in Massive Gravity
• Thermodynamical Properties of Apparent Horizon in Warped DGP Braneworld
• Corrected Entropy-Area Relation and Modified Friedmann Equations
• Holographic duality and the resistivity of strange metals
• Friedmann Equations and Thermodynamics of Apparent Horizons
• Deep Connection Between Thermodynamics and Gravity in Gauss-Bonnet Braneworld
• Momentum dissipation and effective theories of coherent and incoherent transport
• Thermodynamics of Apparent Horizon in Brane World Scenario
• Einstein's equations as a thermodynamic identity: The cases of stationary axisymmetric horizons and evolving spherically symmetric horizons
• Generalized Misner-Sharp quasi-local mass in Einstein-Gauss-Bonnet gravity
• Generalized Vaidya Spacetime in Lovelock Gravity and Thermodynamics on Apparent Horizon
• Thermodynamics in $F(R)$ gravity with phantom crossing
• Thermo-electric transport in gauge/gravity models with momentum dissipation
• The generalized second law of thermodynamics in generalized gravity theories
• F(R) gravity equation of state
• Thermodynamics of Apparent Horizon in Brane World Scenarios
• Charged black holes in nonlinear massive gravity
• Analytic DC thermo-electric conductivities in holography with massive gravitons
• Gravity: A New Holographic Perspective
• Thermodynamics on the apparent horizon in generalized gravity theories
• Hawking-Page transition in holographic massive gravity
• Hydrodynamics of spacetime and vacuum viscosity
• First law of thermodynamics and Friedmann-like equations in braneworld cosmology
• Holographic Superconductor on Q-lattice
• Viscous Cosmology and Thermodynamics of Apparent Horizon
• Thermodynamic Interpretation of Field Equations at Horizon of BTZ Black Hole
• Misner-Sharp Mass in $N$-dimensional $f(R)$ Gravity
• Hawking radiation from the cosmological horizon in a FRW universe
• Black holes and gravitational waves in three-dimensional f(R) gravity
• From thermodynamics to the solutions in gravity theory
• The equation of state for scalar-tensor gravity

Cited by in corpus (26)

• Noncommutative geometry inspired black holes in Rastall gravity
• Holographic Thermalization and Generalized Vaidya-AdS Solutions in Massive Gravity
• Ghost free massive gravity with singular reference metrics
• Holographic Josephson Junction from Massive Gravity
• Influence of inhomogeneities on holographic mutual information and butterfly effect
• The modified first laws of thermodynamics of anti-de Sitter and de Sitter space-times
• Holographic conductivity in the massive gravity with power-law Maxwell field
• Thermodynamics and evaporation of perfect fluid dark matter black hole in phantom background
• Generalized Vaidya Solutions and Misner-Sharp mass for $n$-dimensional massive gravity
• On dRGT massive gravity with degenerate reference metrics
• Quasinormal Modes for Dynamical Black Holes
• First Principle Study of Gravitational Pressure and Thermodynamics of FRW Universe
• Magnetothermoelectric DC conductivities from holography models with hyperscaling factor in Lifshitz spacetime
• Counterterms in Massive Gravity Theory
• The Hawking-Page-like Phase Transition from FRW Spacetime to McVittie Black Hole
• The effects of massive graviton on the equilibrium between the black hole and radiation gas in an isolated box
• The holographic p+ip solution failed to win the competition in dRGT massive gravity
• Insight into the Microstructure of FRW Universe from a $P$-$V$ Phase Transition
• Topological Defects Formation with Momentum Dissipation
• Equation of State and Joule-Thomson Expansion for the FRW Universe in the Brane World Scenario
• Non perturbative spherical gravitational waves
• Thermodynamics in new model of loop quantum cosmology
• Misner-Sharp Energy and P-V Criticality in Quasi-Topological Cosmology
• Cooling-Heating Properties of the FRW Universe in Gravity with a Generalized Conformal Scalar Field
• Time evolving fluid from Vaidya spacetime
• Modifying horizon thermodynamics by surface tensions