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An Entropy Functional for Riemann-Cartan Space-Times

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An Erratum to this article was published on 22 September 2013

Abstract

By viewing space-time as a continuum elastic medium and introducing an entropy functional for its elastic deformations, T. Padmanabhan has shown that general relativity emerges from varying the functional and that the latter suggests holography for gravity and yields the Bekenstein-Hawking entropy formula. In this paper we extend this idea to Riemann-Cartan space-times by constructing an entropy functional for the elastic deformations of space-times with torsion. We show that varying this generalized entropy functional permits to recover the full set of field equations of the Cartan-Sciama-Kibble theory. Our generalized functional shows that the contributions to the on-shell entropy of a bulk region in Riemann-Cartan space-times come from the boundary as well as the bulk and hence does not suggest that holography would also apply for gravity with spin in space-times with torsion. It is nevertheless shown that for the specific cases of Dirac fields and spin fluids the system does become holographic. The entropy of a black hole with spin is evaluated and found to be in agreement with Bekenstein-Hawking formula.

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Authors and Affiliations

  1. Département LMD-ST, Université A. Mira, Route Targa Ouzemmour Béjaia, W. Béjaia, 06000, Algeria

    F. Hammad

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  1. F. Hammad
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Correspondence to F. Hammad.

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An erratum to this article is available at http://dx.doi.org/10.1007/s10773-013-1806-x.

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Hammad, F. An Entropy Functional for Riemann-Cartan Space-Times. Int J Theor Phys 51, 362–373 (2012). https://doi.org/10.1007/s10773-011-0913-9

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