APS xbb Phys. Rev. Lett. xbb Volume 103 xbb Issue 10
Phys. Rev. Lett. 103, 101301 (2009) [4 pages]
Einstein Equations for Generalized Theories of Gravity and the Thermodynamic Relation Q=TS are Equivalent
Ram Brustein1 and Merav Hadad1,2
1Department of Physics, Ben-Gurion University, Beer-Sheva 84105, Israel
2Department of Natural Sciences, The Open University of Israel, P.O.B. 808, Raanana 43107, Israel
Received 9 March 2009; published 1 September 2009
We show that the equations of motion of generalized theories of gravity are equivalent to the thermodynamic relation Q=TS. Our proof relies on extending previous arguments by using a more general definition of the Noether charge entropy. We have thus completed the implementation of Jacobson’s proposal to express Einstein’s equations as a thermodynamic equation of state. Additionally, we find that the Noether charge entropy obeys the second law of thermodynamics if the energy-momentum tensor obeys the null energy condition. Our results support the idea that gravitation on a macroscopic scale is a manifestation of the thermodynamics of the vacuum.
xa92009 The American Physical Society
URL: http://link.aps.org/doi/10.1103/PhysRevLett.103.101301
DOI: 10.1103/PhysRevLett.103.101301
PACS: 04.70.Dy; 04.62.+
v 04.70.Dy Quantum aspects of black holes, evaporation, thermodynamics 04.62.+v Quantum fields in curved spacetime YEAR: 2009
arXiv.org > gr-qc > arXiv:0911.5004
General Relativity and Quantum Cosmology
Thermodynamical Aspects of Gravity: New insights
T.Padmanabhan (Submitted on 26 Nov 2009)
Abstract: The fact that one can associate thermodynamic properties with horizons brings together principles of quantum theory, gravitation and thermodynamics and possibly offers a window to the nature of quantum geometry. This review discusses certain aspects of this topic concentrating on new insights gained from some recent work. After a brief introduction of the overall perspective, Sections 2 and 3 provide the pedagogical background on the geometrical features of bifurcation horizons, path integral derivation of horizon temperature, black hole evaporation, structure of Lanczos-Lovelock models, the concept of Noether charge and its relation to horizon entropy. Section 4 discusses several conceptual issues introduced by the existence of temperature and entropy of the horizons. In Section 5 we take up the connection between horizon thermodynamics and gravitational dynamics and describe several peculiar features which have no simple interpretation in the conventional approach. The next two sections describe the recent progress achieved in an alternative perspective of gravity. In Section 6 we provide a thermodynamic interpretation of the field equations of gravity in any diffeomorphism invariant theory and in Section 7 we obtain the field equations of gravity from an entropy maximization principle. The last section provides a summary.
Submission history
From: T. Padmanabhan [view email]
[v1] Thu, 26 Nov 2009 03:39:55 GMT (118kb)