Padmanabhan, T and Patel, Apoorva (2003) Semiclassical quantization of gravity I: Entropy of horizons and the area spectrum. [Preprint]

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Abstract
The principle of equivalence provides a description of gravity in terms of the metric tensor and determines how gravity affects the light cone structure of the spacetime. This, in turn, leads to the existence of observers (in any spacetime) who do not have access to regions of spacetime bounded by horizons. To take into account this generic possibility, it is necessary to 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. This principle is powerful enough to obtain the following results: (a) The action principle of gravity must be of such a structure that, in the semiclassical limit, the action of the unobserved degrees of freedom reduces to a boundary contribution $A_{\rm boundary}$ obtained by integrating a four divergence. (b) When the boundary is a horizon, $A_{\rm boundary}$ essentially reduces to a single, welldefined, term. (c) This boundary term must have a quantized spectrum with uniform spacing, $\Delta A_{boundary}=2\pi\hbar$, in the semiclassical limit. Using this principle in conjunction with the usual action principle in gravity, we show that: (i) The area of any oneway membrane is quantized. (ii) The information hidden by a oneway membrane leads 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 Physical & Mathematical Sciences > Centre for Theoretical Studies Division of Information Sciences > Supercomputer Education & Research Centre 
Date Deposited:  13 Aug 2004 
Last Modified:  19 Sep 2010 04:13 
URI:  http://eprints.iisc.ernet.in/id/eprint/774 
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