ADM reduction of Einstein action and black hole entropy

Abstract

We reduce the 4D Einstein-Hilbert action to a constant-radius hypersurface of foliation. The resulting theory is a scalar theory defined on a 3D hypersurface of the original black hole background, and has an exponential potential. Once the the hypersurface is located at the Schwarzschild radius, the 3D theory is effectively reduced to a 2D Liouville type theory. We compute {the entropy associated with the hypersurface intrinsic degrees of freedom}, and show that its leading order reproduces the Bekenstein-Hawking area law. The subleading terms come in logarithm/inverse powers of the area.

27 pages, 1 figure, reduction procedure improved and expanded (details in Appendix A), ref added

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Cited by in corpus (10)

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• Boundary dynamics in gravitational theories
• Foliation-based quantization and black hole information
• Foliation-based approach to quantum gravity and applications to astrophysics
• Reduction of BTZ spacetime to hypersurfaces of foliation
• Revisit of renormalization of Einstein-Maxwell theory at one-loop