Kruskal coordinates as canonical variables for Schwarzschild black holes

Details Kruskal coordinates as canonical variables for Schwarzschild black holes Kruskal coordinates as canonical variables for Schwarzschild black holes

2000-11-21

arxiv.org/abs/gr-qc/0011071v1

Phys.Rev. D63 (2001) 084007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages, no figures

Scientific paper

10.1103/PhysRevD.63.084007

We derive a transformation from the usual ADM metric-extrinsic curvature variables on the phase space of Schwarzschild black holes, to new canonical variables which have the interpretation of Kruskal coordinates. We explicitly show that this transformation is non-singular, even at the horizon. The constraints of the theory simplify in terms of the new canonical variables and are equivalent to the vanishing of the canonical momenta. Our work is based on earlier seminal work by Kuchar in which he reconstructed curvature coordinates and a mass function from spherically symmetric canonical data. The key feature in our construction of a nonsingular canonical transformation to Kruskal variables, is the scaling of the curvature coordinate variables by the mass function rather than by the mass at left spatial infinity.

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