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GR: Fachverband Gravitation und Relativitätstheorie
GR 3: Classical General Relativity
GR 3.2: Vortrag
Montag, 16. März 2015, 16:30–16:50, H 2013
Plebański-Demiański solutions of General Relativity and their expressions quadratic and cubic in curvature: analogies to electromagnetism — •Jens Boos — Institute for Theoretical Physics, University of Cologne, 50923 Köln, Germany
An electromagnetic field represented by the field strength 2-form F has two invariants: the scalar B2 − E2 and the pseudo-scalar E · B. These relations taken from (linear) vacuum electrodynamics persist up to the full non-linear case of Einstein’s General Relativity as applied to the exact seven parameter solution of Plebański and Demiański (PD).
The vacuum energy density B2 + E2 corresponding to an electromagnetic field can be deduced from the square of its symmetric energy momentum tensor. The square of the Bel-Robinson tensor gives the analogous expression in case of the PD solution.
We also determine the Kummer tensor, a tensor cubic in curvature, for the PD solution for the first time, and calculate the pieces of its irreducible decomposition.
The calculations are carried out in two coordinate systems: in the original polynomial PD coordinates, and in a modified Boyer-Lindquist-like version introduced by Griffiths and Podolský (GP) allowing for a more straightforward physical interpretation of the free parameters.