Roeken, Christian (2017) Kerr isolated horizons in Ashtekar and Ashtekar-Barbero connection variables. GENERAL RELATIVITY AND GRAVITATION, 49 (9): UNSP 114. ISSN 0001-7701, 1572-9532
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The Ashtekar and Ashtekar-Barbero connection variable formulations of Kerr isolated horizons are derived. Using a regular Kinnersley tetrad in horizonpenetrating Kruskal-Szekeres-like coordinates, the spin coefficients of Kerr geometry are determined by solving the first Maurer-Cartan equation of structure. Isolated horizon conditions are imposed on the tetrad and the spin coefficients. A transformation into an orthonormal tetrad frame that is fixed in the time gauge is applied and explicit calculations of the spin connection, the Ashtekar and Ashtekar-Barbero connections, and the corresponding curvatures on the horizon 2-spheres are performed. Since the resulting Ashtekar-Barbero curvature does not comply with the simple form of the horizon boundary condition of Schwarzschild isolated horizons, i.e., on the horizon 2-spheres, the Ashtekar-Barbero curvature is not proportional to the Plebanski 2-form, which is required for an SU(2) Chern-Simons treatment of the gauge degrees of freedom in the horizon boundary in the context of loop quantum gravity, a general method to construct a new connection whose curvature satisfies such a relation for Kerr isolated horizons is introduced. For the purpose of illustration, this method is employed in the framework of slowly rotating Kerr isolated horizons.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | BLACK-HOLE ENTROPY; QUANTUM-GRAVITY; EXTENSION; GEOMETRY; METRICS; SPACE; SPIN; Kerr isolated horizons; Ashtekar-Barbero connection variables; Horizon boundary condition |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 14 Dec 2018 13:15 |
| Last Modified: | 18 Feb 2019 14:24 |
| URI: | https://pred.uni-regensburg.de/id/eprint/1292 |
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