%0 Journal Article %1 Mei2011Einstein %A Mei, Jianwei %D 2011 %K 4d\_bhs, arxiv, hcs, non-ext-bhs %T Einstein Gravity as a Conformal Field Theory on Horizons of Stationary and Axisymmetric Black Holes %U http://arxiv.org/abs/1108.3841 %X We carry out a Kaluza-Klein reduction of the Einstein-Hilbert action along the ignorable coordinates of stationary and axisymmetric black holes. Rigid diffeomorphism invariance of the \$m\$-ignorable coordinates then become a global \$SL(m,R)\$ gauge symmetry of the reduced theory. Mass and angular momentum of the black holes are related to generators of an \$SL(2,R)\$ subgroup of the full symmetry. Related to each angular momentum there is also an \$SL(2,R)\$ subgroup. On the horizon, this \$SL(2,R)\$ can be extended to the full Witt algebra, which is an exact symmetry of the reduced action when the black hole temperature is zero. So on the horizon, the Kaluza-Klein reduced action is a conformal field theory. The infinite dimensional symmetries are explicitly broken when the system is at a finite temperature, i.e. when the black hole temperature is nonzero.

@article{Mei2011Einstein, abstract = {{We carry out a Kaluza-Klein reduction of the Einstein-Hilbert action along the ignorable coordinates of stationary and axisymmetric black holes. Rigid diffeomorphism invariance of the \$m\$-ignorable coordinates then become a global \$SL(m,R)\$ gauge symmetry of the reduced theory. Mass and angular momentum of the black holes are related to generators of an \$SL(2,R)\$ subgroup of the full symmetry. Related to each angular momentum there is also an \$SL(2,R)\$ subgroup. On the horizon, this \$SL(2,R)\$ can be extended to the full Witt algebra, which is an exact symmetry of the reduced action when the black hole temperature is zero. So on the horizon, the Kaluza-Klein reduced action is a conformal field theory. The infinite dimensional symmetries are explicitly broken when the system is at a finite temperature, i.e. when the black hole temperature is nonzero.}}, added-at = {2019-02-26T10:37:35.000+0100}, archiveprefix = {arXiv}, author = {Mei, Jianwei}, biburl = {https://www.bibsonomy.org/bibtex/29124a5af960feda2a0cc202b6a6db62a/acastro}, citeulike-article-id = {9697754}, citeulike-linkout-0 = {http://arxiv.org/abs/1108.3841}, citeulike-linkout-1 = {http://arxiv.org/pdf/1108.3841}, day = 18, eprint = {1108.3841}, interhash = {3544ed2ae24d576d214c684ee6848a25}, intrahash = {9124a5af960feda2a0cc202b6a6db62a}, keywords = {4d\_bhs, arxiv, hcs, non-ext-bhs}, month = aug, posted-at = {2011-08-22 21:05:38}, priority = {2}, timestamp = {2019-02-26T10:37:35.000+0100}, title = {{Einstein Gravity as a Conformal Field Theory on Horizons of Stationary and Axisymmetric Black Holes}}, url = {http://arxiv.org/abs/1108.3841}, year = 2011 }