Notes on Entropy Force in General Spherically Symmetric Spacetimes

Abstract

In a recent paper [arXiv:1001.0785], Verlinde has shown that the Newton gravity appears as an entropy force. In this paper we show how gravity appears as entropy force in Einstein's equation of gravitational field in a general spherically symmetric spacetime. We mainly focus on the trapping horizon of the spacetime. We find that when matter fields are absent, the change of entropy associated with the trapping horizon indeed can be identified with an entropy force. When matter fields are present, we see that heat flux of matter fields also leads to the change of entropy. Applying arguments made by Verlinde and Smolin, respectively, to the trapping horizon, we find that the entropy force is given by the surface gravity of the horizon. The cases in the untrapped region of the spacetime are also discussed.

revtex4, 21 pages, no figures, one reference added, published version, to appear in Phys.Rev.D

References in corpus (18)

• Thermodynamic Behavior of Friedmann Equation at Apparent Horizon of FRW Universe
• Unified First Law and Thermodynamics of Apparent Horizon in FRW Universe
• Thermodynamic route to Field equations in Lanczos-Lovelock Gravity
• Hawking Radiation of Apparent Horizon in a FRW Universe
• Thermodynamical Properties of Apparent Horizon in Warped DGP Braneworld
• Corrected Entropy-Area Relation and Modified Friedmann Equations
• Friedmann Equations and Thermodynamics of Apparent Horizons
• Deep Connection Between Thermodynamics and Gravity in Gauss-Bonnet Braneworld
• Friedmann Equations from Entropic Force
• 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 Vaidya Spacetime in Lovelock Gravity and Thermodynamics on Apparent Horizon
• Dynamical surface gravity
• Thermodynamics of Apparent Horizon in Brane World Scenarios
• Thermodynamics on the apparent horizon in generalized gravity theories
• First law of thermodynamics and Friedmann-like equations in braneworld cosmology
• Notes Concerning "On the Origin of Gravity and the Laws of Newton" by E. Verlinde (arXiv:1001.0785)
• Thermodynamic Interpretation of Field Equations at Horizon of BTZ Black Hole

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• Dynamics of Gravity as Thermodynamics on the Spherical Holographic Screen
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• On thermal force from holographic action