×

zbMATH — the first resource for mathematics

Topological constraints on Maxwell fields in Robertson-Walker space-times. (English) Zbl 0941.83517
Summary: Two spatially homogeneous solutions of Maxwell’s equations with a source in the elliptic Robertson-Walker (RW) spacetime geometry are found. It is shown that although both solutions can be accommodated in the RW space-time manifolds whose sections \(t=\text{const}\) are three-spheres \(S^3\), only one of them is admissible when the sections are quaternionic manifolds \(Q^3\), making explicit the existence of top ological constraints on Maxwell fields in Robertson-Walker space-times.

MSC:
83C50 Electromagnetic fields in general relativity and gravitational theory
Software:
SHEEP
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Narlikar, J.V.; Seshadri, T.R., Astrophys. J., 288, 43, (1985)
[2] Weeks, J.R., The shape of space, () · Zbl 1030.57001
[3] W.P. Thurston, The geometry and topology of 3-manifolds, Princeton University report, unpublished. · Zbl 0483.57007
[4] Scott, P., Bull. London math. soc., 15, 401, (1983)
[5] Åman, J.E., (), distributed with the CLASSI source · Zbl 0603.53036
[6] MacCallum, M.A.H.; Skea, J.E.F., SHEEP: A computer algebra system for general relativity, () · Zbl 0829.53057
[7] Frick, I., The computer algebra system SHEEP, what it can and cannot do in general relativity, ()
[8] Sommerville, D.M.Y., The elements of non-Euclidean geometry, (1958), Dover New York · Zbl 0086.14102
[9] King, D.H., Phys. rev. D, 44, 2356, (1991)
[10] Costa, J.L.C.; Wolk, I.; Teixeira, A.F.F., Phys. rev. D, 29, 2402, (1984)
[11] Teixeira, A.F.F., Phys. rev. D, 31, 2132, (1985)
[12] Rebouças, M.J.; Teixeira, A.F.F., J. math. phys., 32, 1861, (1991)
[13] Misner, C.W.; Thorne, K.S.; Wheeler, J.A., Gravitation, (1973), Freeman San Francisco
[14] d’Inverno, R.A., Introducing Einstein’s relativity, (1992), Oxford Univ. Press Oxford · Zbl 0776.53046
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.