Gravitational entropy of static space-times and microscopic density of states

Aug, 2003
4 pages
Published in:
  • Class.Quant.Grav. 21 (2004) 4485-4494
e-Print:

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Abstract: (arXiv)
A general ansatz for gravitational entropy can be provided using the criterion that, any patch of area which acts as a horizon for a suitably defined accelerated observer, must have an entropy proportional to its area. After providing a brief justification for this ansatz, several consequences are derived: (i) In any static spacetime with a horizon and associated temperature β1\beta^{-1}, this entropy satisfies the relation S=(1/2)βES=(1/2)\beta E where EE is the energy source for gravitational acceleration, obtained as an integral of (Tab(1/2)Tgab)uaub(T_{ab}-(1/2)Tg_{ab})u^au^b. (ii) With this ansatz of SS, the minimization of Einstein-Hilbert action is equivalent to minimizing the free energy FF with βF=βUS\beta F=\beta U-S where UU is the integral of TabuaubT_{ab}u^au^b. We discuss the conditions under which these results imply SE2S\propto E^2 and/or SU2S\propto U^2 thereby generalizing the results known for black holes. This approach links with several other known results, especially the holographic views of spacetime.
  • space-time: static
  • entropy: gravitation
  • horizon