Universität zu Köln

Boos, Jens ORCID: 0000-0003-3969-900X (2015). Plebanski-Demianski solution of general relativity and its expressions quadratic and cubic in curvature: Analogies to electromagnetism. Int. J. Mod. Phys. D, 24 (10). SINGAPORE: WORLD SCIENTIFIC PUBL CO PTE LTD. ISSN 1793-6594

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Abstract

Analogies between gravitation and electromagnetism have been known since the 1950s. Here, we examine a fairly general type D solution-the exact seven parameter solution of Plebanski-Demianski (PD)-to demonstrate these analogies for a physically meaningful spacetime. The two quadratic curvature invariants B-2 - E-2 and E.B are evaluated analytically. In the asymptotically flat case, the leading terms of E and B can be interpreted as gravitoelectric mass and gravitoelectric current of the PD solution, respectively, if there are no gravitomagnetic monopoles present. Furthermore, the square of the Bel-Robinson tensor reads (B-2 + E-2)(2) for the PD solution, reminiscent of the square of the energy density in electrodynamics. By analogy to the energy-momentum 3-form of the electromagnetic field, we provide an alternative way to derive the recently introduced Bel-Robinson 3-form, from which the Bel-Robinson tensor can be calculated. We also determine the Kummer tensor, a tensor cubic in curvature, for a general type D 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 Podolsky (GP) allowing for a more straightforward physical interpretation of the free parameters.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Boos, Jens UNSPECIFIED orcid.org/0000-0003-3969-900X UNSPECIFIED
URN:	urn:nbn:de:hbz:38-394930
DOI:	10.1142/S0218271815500790
Journal or Publication Title:	Int. J. Mod. Phys. D
Volume:	24
Number:	10
Date:	2015
Publisher:	WORLD SCIENTIFIC PUBL CO PTE LTD
Place of Publication:	SINGAPORE
ISSN:	1793-6594
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language BEL-ROBINSON TENSOR; RIEMANN TENSOR; SPACETIMES; ENERGY; GRAVITY; MASS; FORM Multiple languages Astronomy & Astrophysics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/39493