Dirichlet boundary value problem for Chern-Simons modified gravity
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Chern-Simons modified gravity comprises the Einstein-Hilbert action and a higher-derivative interaction containing the Chern-Pontryagin density. We derive the analog of the Gibbons-Hawking-York boundary term required to render the Dirichlet boundary value problem well-defined. It turns out to be a boundary Chern-Simons action for the extrinsic curvature. We address applications to black hole thermodynamics.
4 pages, revtex4, v2: added Refs., made one statement stronger, added footnote and added paragraph on single field inflation
4 pages, revtex4, v2: added Refs., made one statement stronger, added footnote and added paragraph on single field inflation