Thermodynamic Behavior of Friedmann Equation at Apparent Horizon of FRW Universe

Abstract

It is shown that the differential form of Friedmann equation of a FRW universe can be rewritten as a universal form $dE=TdS+WdV$ at apparent horizon, where $E$ and $V$ are the matter energy and volume inside the apparent horizon (the energy $E$ is the same as the Misner-Sharp energy in the case of Einstein general relativity), $W=(\rho -P)/2$ is the work density and $\rho$ and $P$ are energy density and pressure of the matter in the universe, respectively. From the thermodynamic identity one can derive that the apparent horizon has associated entropy $S=A/4G$ and temperature $T=\kappa /2\pi$ in Einstein general relativity, where $A$ is the area of apparent horizon and $\kappa$ is the surface gravity at apparent horizon. We extend our procedure to the Gauss-Bonnet gravity and more general Lovelock gravity and show that the differential form of Friedmann equations in these gravities can also be rewritten to thee universal form $dE=TdS+WdV$ at the apparent horizon with entropy $S$ being given by expression previously known via black hole thermodynamics.

v4: Revtex, 18 pages, to appear in PRD

References in corpus (27)

• Thermodynamics of Spacetime: The Einstein Equation of State
• Black Hole Entropy is Noether Charge
• Gauss-Bonnet Black Holes in AdS Spaces
• First Law of Thermodynamics and Friedmann Equations of Friedmann-Robertson-Walker Universe
• Unified first law of black-hole dynamics and relativistic thermodynamics
• Gravity and the Thermodynamics of Horizons
• Classical and Quantum Thermodynamics of horizons in spherically symmetric spacetimes
• Cosmic Holography
• 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
• Black Hole Scan
• A Note on Thermodynamics of Black Holes in Lovelock Gravity
• Thermodynamics of an accelerated expanding universe
• Dynamic black-hole entropy
• Cosmology and the S-matrix
• Inflation and de Sitter Thermodynamics
• Dimensionally Continued Black Holes
• Topological black holes in the dimensionally continued gravity
• Gauss-Bonnet Black Holes in dS Spaces
• Cardy-Verlinde Formula and Thermodynamics of Black Holes in de Sitter Spaces
• Black holes with topologically nontrivial AdS asymptotics
• Transplanckian energy production and slow roll inflation
• Cardy-Verlinde Formula and Asymptotically de Sitter Spaces
• Holography of Gravitational Action Functionals
• Gravity: A New Holographic Perspective
• de Sitter thermodynamics and the braneworld
• Holography and Entropy Bounds in Gauss-Bonnet Gravity

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