×

Algebraically special hypersurface-homogeneous Einstein spaces in general relativity. (English) Zbl 0751.53016

The authors’ abstract: “This paper illustrates the value of the Newman- Penrose complex null tetrad formalism by using it to obtain all algebraically special Einstein spaces admitting three-parameter groups of motions acting on timelike surfaces containing the repeated principal null direction. Taken together with earlier work, this enables us to give a complete list of Einstein spaces, which are both, algebraically special and hypersurface-homogeneous or homogeneous”.
Reviewer: E.Malec (Kraków)

MSC:

53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
83C20 Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory

Software:

REDUCE
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Newman, E. T.; Penrose, R., An approach to gravitational radiation by a method of spin coefficients, J. Math. Phys., 3, 566 (1962) · Zbl 0108.40905
[2] Penrose, R., A spinor approach to general relativity, Ann. Phys. (NY), 10, 171 (1960) · Zbl 0091.21404
[3] LeBrun, C. R., Ambi-twistors and Einstein’s equations, Class. Quant. Grav., 2, 555 (1985) · Zbl 0575.53028
[4] Penrose, R.; Rindler, W., Spinors and Space-time II: Spinor and Twistor Methods in Space-time Geometry (1985), Cambridge University Press: Cambridge University Press London, New York
[5] MacCallum, M. A.H.; Siklos, S. T.C., Homogeneous and hypersurface-homogeneous algebraically-special Einstein spaces, (Schmutzer, E., Abstracts of Contributed Papers 9th Intern. Conf on General Relativity and Gravitation, Vol. 1 (1980), Intern. Soc. on General Relativity and Gravitation: Intern. Soc. on General Relativity and Gravitation Jena), 54-55 · Zbl 0751.53016
[6] Kramer, D.; Stephani, H.; MacCallum, M. A.H.; Herlt, E., Exact Solutions of Einstein’s Field Equations (1980), Deutscher Verlag der Wissenschaften, Berlin, and Cambridge University Press: Deutscher Verlag der Wissenschaften, Berlin, and Cambridge University Press London, New York, [Russian edition: ed. V.S. Vladimirov (Energoizdat, Moscow, 1982)] · Zbl 0449.53018
[7] Cahen, M.; Defrise, L., Lorentzian four-dimensional manifolds with “local isotropy”, Commun. Math. Phys., 11, 56 (1968) · Zbl 0176.55501
[8] MacCallum, M. A.H., Locally isotropic spacetimes with non-null homogeneous hypersurfaces, (Tipler, F. J., Essays in General Relativity (A Festschrift for A.H. Taub) (1980), Academic Press: Academic Press New York) · Zbl 0467.53025
[9] Barnes, A., On space-times admitting a three-parameter isometry group with two-dimensional null orbits, J. Phys. A, 12, 1493 (1979)
[10] Siklos, S. T.C., Some Einstein spaces and their global properties, J. Phys. A, 14, 395 (1981)
[11] Kramer, D., Einstein-Maxwell fields with null Killing vector, Acta. Phys. Hung., 43, 125 (1977)
[12] Bampi, F.; Cianci, R., Generalized axisymmetric spacetimes, Commun. Math. Phys., 70, 69 (1979)
[13] Hoffman, R. B., Stationary axially symmetric generalizations of the Weyl solutions in general relativity, Phys. Rev., 182, 1361 (1969)
[14] Harness, R. S., Space-times homogeneous on a timelike hypersurface, (Univ. of London Ph.D. Thesis (1982), Queen Mary College) · Zbl 0477.53057
[15] Siklos, S. T.C., Lobatchevski plane gravitational waves, (MacCallum, M. A.H., Galaxies, Axisymmetric Systems and Relativity (Essays presented to W. B. Bonnor on his 65th birthday) (1985), Cambridge University Press: Cambridge University Press London), 247-274 · Zbl 0737.53075
[16] S.T.C. Siklos, Spacetimes with timelike homogeneous hypersurfaces, in preparation.; S.T.C. Siklos, Spacetimes with timelike homogeneous hypersurfaces, in preparation.
[17] Brans, C. H., Complete integrability conditions of the Einstein Petrov equations, type I, J. Math. Phys., 18, 1378 (1977) · Zbl 0353.53015
[18] Papapetrou, A., Les relations identiques entre les equations du formalisme de Newman-Penrose, C.R. Acad. Sci. Paris A, 272, 1613 (1971)
[19] Kinnersley, W., Type D vacuum metrics, J. Math. Phys., 10, 1195 (1969) · Zbl 0182.30202
[20] MacCallum, M. A.H., Computer-aided classification of exact solutions in general relativity, (Cianci, R.; de Ritis, R.; Francaviglia, M.; Marmo, G.; Rubano, C.; Scudellaro, P., General Relativity and Gravitational Physics (9th Italian Conf.) (1991), World Scientific: World Scientific Singapore) · Zbl 0693.53032
[21] Aman, J. E., Manual for CLASSI: classification programs in general relativity (1987), Univ. of Stockholm, Institute of Theoretical Physics report
[22] Debever, R.; Kamran, N.; McLenaghan, R., A single expression for the general solution of Einstein’s vacuum and electrovac field equations with cosmological constant for Petrov type D admitting a non-singular aligned Maxwell field, Phys. Lett. A, 93, 399 (1983)
[23] Hearn, A. C., REDUCE User’s Manual (1987), Rand Corp. CP78: Rand Corp. CP78 Santa Monica, CA, Version 3.3
[24] Kaigorodov, V. R., Einstein spaces of maximum mobility, Dokl. Akad. Nauk. SSSR, 146, 793 (1962), (in Russian) · Zbl 0122.22004
[25] Patera, J.; Winternitz, P., Subalgebras of real three- and four-dimensional Lie algebras, J. Math. Phys., 18, 1449 (1977) · Zbl 0412.17007
[26] van Stockum, W. J., The gravitational field of a distribution of particles rotating about an axis of symmetry, (Proc. R. Soc. Edingburgh A, 57 (1937)), 135 · Zbl 0016.28302
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.