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Title: Thermodynamic behavior of the Friedmann equation at the apparent horizon of the FRW universe

Abstract

It is shown that the differential form of Friedmann equation of a FRW universe can be rewritten as the first law of thermodynamics dE=TdS+WdV at apparent horizon, where E={rho}V is the total energy of matter inside the apparent horizon, V is the volume inside the apparent horizon, W=({rho}-P)/2 is the work density, {rho} and P are energy density and pressure of matter in the universe, respectively. From the thermodynamic identity one can derive that the apparent horizon r-tilde{sub A} 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 of FRW universe. 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 written as dE=TdS+WdV at the apparent horizon of FRW universe with entropy S being given by expression previously known via black hole thermodynamics.

Authors:
;  [1]
  1. Institute of Theoretical Physics, Chinese Academy of Sciences, P.O. Box 2735, Beijing 100080 (China)
Publication Date:
OSTI Identifier:
21020372
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevD.75.084003; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BLACK HOLES; COSMOLOGY; ENERGY DENSITY; ENTROPY; FIELD EQUATIONS; GENERAL RELATIVITY THEORY; GRAVITATION; NONLUMINOUS MATTER; THERMODYNAMICS; UNIVERSE

Citation Formats

Akbar, M., and Cai Ronggen. Thermodynamic behavior of the Friedmann equation at the apparent horizon of the FRW universe. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.084003.
Akbar, M., & Cai Ronggen. Thermodynamic behavior of the Friedmann equation at the apparent horizon of the FRW universe. United States. doi:10.1103/PHYSREVD.75.084003.
Akbar, M., and Cai Ronggen. Sun . "Thermodynamic behavior of the Friedmann equation at the apparent horizon of the FRW universe". United States. doi:10.1103/PHYSREVD.75.084003.
@article{osti_21020372,
title = {Thermodynamic behavior of the Friedmann equation at the apparent horizon of the FRW universe},
author = {Akbar, M. and Cai Ronggen},
abstractNote = {It is shown that the differential form of Friedmann equation of a FRW universe can be rewritten as the first law of thermodynamics dE=TdS+WdV at apparent horizon, where E={rho}V is the total energy of matter inside the apparent horizon, V is the volume inside the apparent horizon, W=({rho}-P)/2 is the work density, {rho} and P are energy density and pressure of matter in the universe, respectively. From the thermodynamic identity one can derive that the apparent horizon r-tilde{sub A} 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 of FRW universe. 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 written as dE=TdS+WdV at the apparent horizon of FRW universe with entropy S being given by expression previously known via black hole thermodynamics.},
doi = {10.1103/PHYSREVD.75.084003},
journal = {Physical Review. D, Particles Fields},
number = 8,
volume = 75,
place = {United States},
year = {Sun Apr 15 00:00:00 EDT 2007},
month = {Sun Apr 15 00:00:00 EDT 2007}
}