Twistor Theory and the Einstein Equations
R. Penrose (in Advances in twistor theory, pp. 168‒176, and in Cosmology and gravitation; Nato advanced study institute series, pp. 287‒316 (1980). New York: Plenum Press) has argued that the goal of twistor theory with regard to the vacuum Einstein equations ought to consist of some kind of unifica...
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| Veröffentlicht in: | Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences Mathematical and physical sciences, 1985-05, Vol.399 (1816), p.111-134 |
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| container_issue | 1816 |
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| container_title | Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences |
| container_volume | 399 |
| creator | Law, P. R. |
| description | R. Penrose (in Advances in twistor theory, pp. 168‒176, and in Cosmology and gravitation; Nato advanced study institute series, pp. 287‒316 (1980). New York: Plenum Press) has argued that the goal of twistor theory with regard to the vacuum Einstein equations ought to consist of some kind of unification of twistor-theoretic descriptions of anti-self-dual (a. s. d. ) and self-dual (s. d. ) space-times. S. d. space‒times currently possess a description only in terms of dual twistor space, however, rather than twistor space. In this paper, suggestions due to Penrose for providing a purely twistor space description of s. d. space‒times are investigated. It is shown how the points of certain s. d. space‒times define mappings on twistor space and the geometry of these mappings is studied. The families of mappings for two particular s. d. space‒times are presented explicitly. |
| doi_str_mv | 10.1098/rspa.1985.0050 |
| format | Article |
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The families of mappings for two particular s. d. space‒times are presented explicitly.</description><subject>Ambiguity</subject><subject>Coordinate systems</subject><subject>Dyadic relations</subject><subject>Einstein equations</subject><subject>Geometric lines</subject><subject>Geometric planes</subject><subject>Loci</subject><subject>Mathematical duality</subject><subject>Spacetime</subject><subject>Tangents</subject><issn>1364-5021</issn><issn>0080-4630</issn><issn>1471-2946</issn><issn>2053-9169</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1985</creationdate><recordtype>article</recordtype><recordid>eNp9Uc2L1DAUL6Lgunr15KFXDx3zmu-TLMs4CgOKjuLtEdPUyTg2Nem41r_etJWFQdxTXni_z6QongJZAdHqRUy9WYFWfEUIJ_eKC2ASqlozcT_PVLCKkxoeFo9SOhBCNFfyoni-u_FpCLHc7V2IY2m6phz2rlz7Lg3Od-X6x8kMPnTpcfGgNcfknvw9L4uPr9a769fV9u3mzfXVtrJMqqECRmsnW6FaZYkwkmvRfFHMUWtba7UFJw1lnAitTMMIl0Ry4TRvOLOgW04vi9Wia2NIKboW--i_mzgiEJyK4lQUp6I4Fc0EuhBiGHOwYL0bRjyEU-zy9f-sdBfr_Yd3V6CF_km19qBAIFEUiMxjjb99P8tNAMwA9CmdHM6wc5t_XZ8trofp0W-b1VRLSVheV8s6_4n7dbs28RsKSSXHT4rhZyo139Yb3GT8ywW_91_3Nz46PGszm9vQDa4b5pxzQgDA9nQ8Yt-0WQHuVAhjH5M5I9M_TMK8yQ</recordid><startdate>19850508</startdate><enddate>19850508</enddate><creator>Law, P. 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R.</creatorcontrib><collection>Istex</collection><collection>CrossRef</collection><jtitle>Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Law, P. R.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Twistor Theory and the Einstein Equations</atitle><jtitle>Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences</jtitle><stitle>Proc. R. Soc. Lond. A</stitle><addtitle>Proc. R. Soc. Lond. A</addtitle><date>1985-05-08</date><risdate>1985</risdate><volume>399</volume><issue>1816</issue><spage>111</spage><epage>134</epage><pages>111-134</pages><issn>1364-5021</issn><issn>0080-4630</issn><eissn>1471-2946</eissn><eissn>2053-9169</eissn><abstract>R. Penrose (in Advances in twistor theory, pp. 168‒176, and in Cosmology and gravitation; Nato advanced study institute series, pp. 287‒316 (1980). New York: Plenum Press) has argued that the goal of twistor theory with regard to the vacuum Einstein equations ought to consist of some kind of unification of twistor-theoretic descriptions of anti-self-dual (a. s. d. ) and self-dual (s. d. ) space-times. S. d. space‒times currently possess a description only in terms of dual twistor space, however, rather than twistor space. In this paper, suggestions due to Penrose for providing a purely twistor space description of s. d. space‒times are investigated. It is shown how the points of certain s. d. space‒times define mappings on twistor space and the geometry of these mappings is studied. 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| ispartof | Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences, 1985-05, Vol.399 (1816), p.111-134 |
| issn | 1364-5021 0080-4630 1471-2946 2053-9169 |
| language | eng |
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| source | JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing |
| subjects | Ambiguity Coordinate systems Dyadic relations Einstein equations Geometric lines Geometric planes Loci Mathematical duality Spacetime Tangents |
| title | Twistor Theory and the Einstein Equations |
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