Padmanabhan, T and Patel, Apoorva (2003) Role of Horizons in Semiclassical Gravity: Entropy and the Area Spectrum. [Preprint]

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Abstract
In any spacetime, it is possible to have a family of observers who have access to only part of the spacetime manifold, because of the existence of a horizon. We demand that physical theories in a given coordinate system must be formulated entirely in terms of variables that an observer using that coordinate system can access. In the coordinate frame in which these observers are at rest, the horizon manifests itself as a (coordinate) singularity in the metric tensor. Regularization of this singularity removes the inaccessible region, and leads to the following consequences: (a) The nontrivial topological structure for the effective manifold allows one to obtain the standard results of quantum field theory in curved spacetime. (b) In case of gravity, this principle requires that the effect of the unobserved degrees of freedom should reduce to a boundary contribution $A_{\rm boundary}$ to the gravitational action. When the boundary is a horizon, $A {\rm boundary}$ reduces to a single, welldefined term proportional to the area of the horizon. Using the form of this boundary term, it is possible to obtain the full gravitational action in the semiclassical limit. (c) This boundary term must have a quantized spectrum with uniform spacing, $\Delta A_{boundary}=2\pi\hbar$, in the semiclassical limit. This, in turn, yields the following results for semiclassical gravity: (i) The area of any oneway membrane is quantized. (ii) The information hidden by a oneway membrane amounts to an entropy, which is always onefourth of the area of the membrane in the leading order. (iii) In static spacetimes, the action for gravity can be given a purely thermodynamic interpretation and the Einstein equations have a formal similarity to laws of thermodynamics.
Item Type:  Preprint 

Department/Centre:  Division of Interdisciplinary Sciences > Supercomputer Education & Research Centre Division of Physical & Mathematical Sciences > Centre for Theoretical Studies (Ceased to exist at the end of 2003) 
Date Deposited:  25 Aug 2008 
Last Modified:  19 Sep 2010 04:13 
URI:  http://eprints.iisc.ac.in/id/eprint/768 
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