Thermodynamics of Black Holes from Equipartition of Energy and Holography

Abstract

A gravitational potential in the relativistic case is introduced as an alternative to Wald's potential used by Verlinde, which reproduces the familiar entropy/area relation S=A/4 (in the natural units) when Verlinde's idea is applied to the black hole case. Upon using the equipartition rule, the correct form of the Komar mass (energy) can also be obtained, which leads to the Einstein equations. It is explicitly shown that our entropy formula agrees with Verlinde's entropy variation formula in spherical cases. The stationary space-times, especially the Kerr-Newman black hole, are then discussed, where it is shown that the equipartition rule involves the reduced mass, instead of the ADM mass, on the horizon of the black hole.

13 pages, a discussion is added into section III in the new version, which explicitly shows that our entropy formula agrees with Verlinde's entropy variation formula in spherical cases. The abstract, introduction and conluding remarks also have been revised. Some typing mistakes in old versions have been corrected. v4: minor modifications, match the published version.

References in corpus (8)

• Friedmann Equations from Entropic Force
• Newtonian gravity in loop quantum gravity
• Quasi-black holes: definition and general properties
• Notes Concerning "On the Origin of Gravity and the Laws of Newton" by E. Verlinde (arXiv:1001.0785)
• Collapsing and static thin massive charged dust shells in a Reissner-Nordström black hole background in higher dimensions
• Gravitational magnetic monopoles and Majumdar-Papapetrou stars
• Towards a Holographic Description of Inflation and Generation of Fluctuations from Thermodynamics
• Entropic force in the presence of black hole

Cited by in corpus (13)

• Lessons from Classical Gravity about the Quantum Structure of Spacetime
• Cosmological Constraints on the Modified Entropic Force Model
• Entropic force and entanglement system
• Debye entropic force and modified Newtonian dynamics
• Dilatonic Entropic Force
• The Friedmann equation in modified entropy-area relation from entropy force
• First law of thermodynamics on holographic screens in entropic force frame
• Does entropic force always imply the Newtonian force law?
• Dynamics of Gravity as Thermodynamics on the Spherical Holographic Screen
• Influence on the entropic force by the virtual degree of freedom on the holographic screen
• On thermal force from holographic action
• Unification of Dark Matter and Dark Energy in a Modified Entropic Force Model
• The modified wave function of test particle approaching holographic screen from entropy force