New variables for classical and quantum gravity in all dimensions: V. Isolated horizon boundary degrees of freedom
Abstract
In this paper, we generalize the treatment of isolated horizons in loop quantum gravity, resulting in a ChernSimons theory on the boundary in the fourdimensional case, to nondistorted isolated horizons in 2(n + 1)dimensional spacetimes. The key idea is to generalize the fourdimensional isolated horizon boundary condition by using the Euler topological density E^{(2n)} of a spatial slice of the black hole horizon as a measure of distortion. The resulting symplectic structure on the horizon coincides with the one of higherdimensional SO(2(n + 1))ChernSimons theory in terms of a Peldantype hybrid connection Γ^{0} and resembles closely the usual treatment in (3 + 1) dimensions. We comment briefly on a possible quantization of the horizon theory. Here, some subtleties arise since higherdimensional nonAbelian ChernSimons theory has local degrees of freedom. However, when replacing the natural generalization to higher dimensions of the usual boundary condition by an equally natural stronger one, it is conceivable that the problems originating from the local degrees of freedom are avoided, thus possibly resulting in a finite entropy.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 March 2014
 DOI:
 10.1088/02649381/31/5/055002
 arXiv:
 arXiv:1304.2679
 Bibcode:
 2014CQGra..31e5002B
 Keywords:

 04.50.Gh;
 11.15.Yc;
 04.60.m;
 loop quantum gravity;
 higher dimensions;
 black holes;
 ChernSimons theory;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 49 pages. v2. journal version. Reference added