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 rtilde{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 GaussBonnet 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:
 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 rtilde{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 GaussBonnet 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}
}

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