1202.0966 (Fayçal Hammad)

An Entropy Functional for Riemann-Cartan Space-Times    [PDF]

Fayçal Hammad

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.

View original: http://arxiv.org/abs/1202.0966