Energy, entropy and the Ricci flow

Samuel, J.; Roy Chowdhury, Sutirtha

Please use this identifier to cite or link to this item: http://hdl.handle.net/2289/3536

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DC Field	Value	Language
dc.contributor.author	Samuel, J.	-
dc.contributor.author	Roy Chowdhury, Sutirtha	-
dc.date.accessioned	2008-05-30T07:40:29Z	-
dc.date.available	2008-05-30T07:40:29Z	-
dc.date.issued	2008-01	-
dc.identifier.citation	Classical and Quantum Gravity, 2008, Vol.25, 035012	en
dc.identifier.issn	E-ISSN: 1361-6382	-
dc.identifier.issn	P-ISSN: 0264-9381	-
dc.identifier.uri	http://hdl.handle.net/2289/3536	-
dc.description	Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations)	en
dc.description.abstract	The Ricci flow (RF) is a heat equation for metrics, which has recently been used to study the topology of closed three-manifolds. In this paper we apply Ricci flow techniques to general relativity. We view a three-dimensional asymptotically flat Riemannian metric as a time symmetric initial data set for Einstein's equations. We study the evolution of the area {\cal A} and Hawking mass {\cal M}_H of a two-dimensional closed surface under the Ricci flow. The physical relevance of our study derives from the fact that in general relativity the area of apparent horizons is related to black hole entropy and the Hawking mass of an asymptotic round 2-sphere is the ADM energy. We begin by considering the special case of spherical symmetry to develop a physical feel for the geometric quantities involved. We then consider a general asymptotically flat Riemannian metric and derive an inequality \frac{{\rm d}}{{\rm d}\tau}{\cal A}^{3/2}\le -24\pi^{3/2} {\cal M}_H which relates the evolution of the area of a closed surface S to its Hawking mass. We suggest that there may be a maximum principle which governs the long-term existence of the asymptotically flat Ricci flow.	en
dc.format.extent	236969 bytes	-
dc.format.mimetype	application/pdf	-
dc.language.iso	en	en
dc.publisher	Institute of Physics Publishing (IOP)	en
dc.relation.uri	http://in.arxiv.org/abs/0711.0430	en
dc.relation.uri	http://dx.doi.org/10.1088/0264-9381/25/3/035012	en
dc.rights	2008 IOP Publishing	en
dc.title	Energy, entropy and the Ricci flow	en
dc.type	Article	en
Appears in Collections:	Research Papers (TP)

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