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A Neumann boundary term for gravity

Krishnan, Chethan and Raju, Avinash (2017) A Neumann boundary term for gravity. In: MODERN PHYSICS LETTERS A, 32 (14).

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Official URL: http://dx.doi.org/10.1142/S0217732317500778

Abstract

The Gibbons-Hawking-York (GHY) boundary term makes the Dirichlet problem for gravity well-defined, but no such general term seems to be known for Neumann boundary conditions. In this paper, we view Neumann not as fixing the normal derivative of the metric (''velocity'') at the boundary, but as fixing the functional derivative of the action with respect to the boundary metric (''momentum''). This leads directly to a new boundary term for gravity: the trace of the extrinsic curvature with a specific dimension-dependent coefficient. In three dimensions, this boundary term reduces to a ``one-half'' GHY term noted in the literature previously, and we observe that our action translates precisely to the Chern-Simons action with no extra boundary terms. In four dimensions, the boundary term vanishes, giving a natural Neumann interpretation to the standard Einstein-Hilbert action without boundary terms. We argue that in light of AdS/CFT, ours is a natural approach for defining a ``microcanonical'' path integral for gravity in the spirit of the (pre-AdS/CFT) work of Brown and York.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the WORLD SCIENTIFIC PUBL CO PTE LTD, 5 TOH TUCK LINK, SINGAPORE 596224, SINGAPORE
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Depositing User: Id for Latest eprints
Date Deposited: 03 Jun 2017 09:33
Last Modified: 03 Jun 2017 09:33
URI: http://eprints.iisc.ac.in/id/eprint/57085

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