ADM reduction of Einstein action and black hole entropy
High Energy Physics - Theory
2014-11-05 v5
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.
Keywords
Cite
@article{arxiv.1304.0014,
title = {ADM reduction of Einstein action and black hole entropy},
author = {I. Y. Park},
journal= {arXiv preprint arXiv:1304.0014},
year = {2014}
}
Comments
27 pages, 1 figure, reduction procedure improved and expanded (details in Appendix A), ref added