1303.2548 (Christian Röken)
Christian Röken
A construction of both self-dual SL(2, C) and SU(2) connection variable formulations for the description of the degrees of freedom of classical, rotating Kerr isolated horizon geometries is presented. These descriptions are based on sets of connection Hamiltonian variables instead of the spacetime metric. The analysis is motivated in a concrete, physical manner based on the stationary, axisymmetric Kerr solution of the vacuum Einstein equations, evaluated in a proper, well-defined frame of reference, on which isolated horizon boundary conditions are imposed. Having derived the kinematical part of such an isolated horizon phase space setting, one can set up a conserved presymplectic structure for the study of dynamical aspects of black hole theory. Since black holes play a crucial role in various fields like quantum gravity, mathematical physics, astrophysics and cosmology, or numerical relativity, one has to deal with different models describing these objects. The quasi-local framework studied in this paper is appropriate for covering most of the physical settings involving black hole dynamics. Moreover, the SU(2) connection variable formulation of classical Kerr isolated horizons allows directly for a semiclassical treatment of rotating quantum black holes in the context of loop quantum gravity.
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http://arxiv.org/abs/1303.2548
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