Entropy of static spacetimes and microscopic density of states

By Thanu Padmanabhan. 2003

218 citations recorded by the source corpus.

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 β−1, this entropy satisfies the relation S = (1/2)βE where E is the energy source for gravitational acceleration, obtained as an integral of (Tab − (1/2)Tgab)uaub. (ii) With this ansatz of S, the minimization of Einstein–Hilbert action is equivalent to minimizing the free energy F with βF = βU − S where U is the integral of Tabuaub. We discuss the conditions under which these results imply S ∝ E2 and/or S ∝ U2 thereby generalizing the results known for black holes. This approach links with several other known results, especially the holographic views of spacetime.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8a4ab77e4633942267542d4ccd5945f1c57e9587

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In Geometry and Topology

T.Padmanabhan

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Friedmann Equations from Entropic Force (2010, background): “He observed that the equipartition law of energy for the horizon degrees of freedom combing with the thermodynamic relation S = E/2T , also leads to the Newton’s law of gravity, here S and T are thermodynamic entropy and temperature associated with the horizon and E is the active gravitational mass ”
Gravity and the Thermodynamics of Horizons (2003, background): “In fact, this paradigm arises very naturally for any staticspacetime with a horizon [161].”
Gravity and the thermodynamics of horizons (2005, background): “olids are [159,160]. This suggests that spacetime dynamics is like the thermodynamic limit in solid state physics. In fact, this paradigm arises very naturally for any static spacetime with a horizon [161]. Such a spacetime has a metric in Eq. (4) with the horizon occurring at the surface N = 0 and ”