Harmonic mappings of Riemannian manifolds and stationary vacuum space–times with whole cylinder symmetry

We consider stationary, cylindrically‐symmetric gravitational fields in the framework of harmonic mappings of Riemannian manifolds. In this approach the emphasis is on a correspondence between the solution of the Einstein field equations and the geodesics in an appropriate Riemannian configuration s...

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Veröffentlicht in:	J. Math. Phys. (N.Y.), v. 16, no. 7, pp. 1431-1434 v. 16, no. 7, pp. 1431-1434, 1975-07, Vol.16 (7), p.1431-1434
Hauptverfasser:	Eriş, Ahmet, Nutku, Yavuz
Format:	Artikel
Sprache:	eng
Schlagworte:	CYLINDRICAL CONFIGURATION EINSTEIN FIELD EQUATIONS- GRAVITATIONAL FIELDS GENERAL RELATIVITY THEORY HAMILTON-JACOBI EQUATIONS METRICS N76300 -Physics (Theoretical)-Gravitation & General Relativity RIEMANN SPACE SPACE-TIME
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container_title	J. Math. Phys. (N.Y.), v. 16, no. 7, pp. 1431-1434
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creator	Eriş, Ahmet Nutku, Yavuz
description	We consider stationary, cylindrically‐symmetric gravitational fields in the framework of harmonic mappings of Riemannian manifolds. In this approach the emphasis is on a correspondence between the solution of the Einstein field equations and the geodesics in an appropriate Riemannian configuration space. Using Hamilton–Jacobi techniques, we obtain the geodesics and construct the resulting space–time geometries. We find that the light cone structure of the configuration space delineates the distinct exterior fields of Lewis and van Stockum which together form the most general solution with whole cylinder symmetry.
doi_str_mv	10.1063/1.522689
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In this approach the emphasis is on a correspondence between the solution of the Einstein field equations and the geodesics in an appropriate Riemannian configuration space. Using Hamilton–Jacobi techniques, we obtain the geodesics and construct the resulting space–time geometries. We find that the light cone structure of the configuration space delineates the distinct exterior fields of Lewis and van Stockum which together form the most general solution with whole cylinder symmetry.</description><identifier>ISSN: 0022-2488</identifier><identifier>EISSN: 1089-7658</identifier><identifier>DOI: 10.1063/1.522689</identifier><identifier>CODEN: JMAPAQ</identifier><language>eng</language><publisher>United States</publisher><subject>CYLINDRICAL CONFIGURATION ; EINSTEIN FIELD EQUATIONS- GRAVITATIONAL FIELDS ; GENERAL RELATIVITY THEORY ; HAMILTON-JACOBI EQUATIONS ; METRICS ; N76300 -Physics (Theoretical)-Gravitation & General Relativity ; RIEMANN SPACE ; SPACE-TIME</subject><ispartof>J. Math. 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(N.Y.), v. 16, no. 7, pp. 1431-1434, 1975-07, Vol.16 (7), p.1431-1434</ispartof><rights>American Institute of Physics</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c322t-b2d95dc10710f283eab8ec7ed776c9991d139fd2e616cd1b5bc36328f2e833093</citedby><cites>FETCH-LOGICAL-c322t-b2d95dc10710f283eab8ec7ed776c9991d139fd2e616cd1b5bc36328f2e833093</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://pubs.aip.org/jmp/article-lookup/doi/10.1063/1.522689$$EHTML$$P50$$Gscitation$$H</linktohtml><link.rule.ids>314,780,784,885,1558,27922,27923,76160</link.rule.ids><backlink>$$Uhttps://www.osti.gov/biblio/4221844$$D View this record in Osti.gov$$Hfree_for_read</backlink></links><search><creatorcontrib>Eriş, Ahmet</creatorcontrib><creatorcontrib>Nutku, Yavuz</creatorcontrib><creatorcontrib>Department of Physics, Middle East Technical University, Ankara, Turkey</creatorcontrib><title>Harmonic mappings of Riemannian manifolds and stationary vacuum space–times with whole cylinder symmetry</title><title>J. Math. Phys. (N.Y.), v. 16, no. 7, pp. 1431-1434</title><description>We consider stationary, cylindrically‐symmetric gravitational fields in the framework of harmonic mappings of Riemannian manifolds. In this approach the emphasis is on a correspondence between the solution of the Einstein field equations and the geodesics in an appropriate Riemannian configuration space. Using Hamilton–Jacobi techniques, we obtain the geodesics and construct the resulting space–time geometries. We find that the light cone structure of the configuration space delineates the distinct exterior fields of Lewis and van Stockum which together form the most general solution with whole cylinder symmetry.</description><subject>CYLINDRICAL CONFIGURATION</subject><subject>EINSTEIN FIELD EQUATIONS- GRAVITATIONAL FIELDS</subject><subject>GENERAL RELATIVITY THEORY</subject><subject>HAMILTON-JACOBI EQUATIONS</subject><subject>METRICS</subject><subject>N76300 -Physics (Theoretical)-Gravitation & General Relativity</subject><subject>RIEMANN SPACE</subject><subject>SPACE-TIME</subject><issn>0022-2488</issn><issn>1089-7658</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1975</creationdate><recordtype>article</recordtype><recordid>eNp90MtKAzEYBeAgCtYq-AjBlS6m5jKXzFKKWqEgiK5DJsnYlEkyTNKW2fkOvqFP4tSRbgRXP_x8HDgHgEuMZhjl9BbPMkJyVh6BCUasTIo8Y8dgghAhCUkZOwVnIawRwpil6QSsF6Kz3hkJrWhb494D9DV8MdoK54xww9uZ2jcqQOEUDFFE453oergVcrOxMLRC6q-Pz2isDnBn4gruVr7RUPaNcUp3MPTW6tj15-CkFk3QF793Ct4e7l_ni2T5_Pg0v1smkhISk4qoMlMSowKjmjCqRcW0LLQqilyWZYkVpmWtiM5xLhWuskrSnBJWE80oRSWdgqsx14doeJAmarmS3jktI08J2Rcf0PWIZOdD6HTN287YoRfHiO-H5JiPQw70ZqT7qJ_6B7v13cHxVtX_2T-53wRyg_M</recordid><startdate>197507</startdate><enddate>197507</enddate><creator>Eriş, Ahmet</creator><creator>Nutku, Yavuz</creator><scope>AAYXX</scope><scope>CITATION</scope><scope>OTOTI</scope></search><sort><creationdate>197507</creationdate><title>Harmonic mappings of Riemannian manifolds and stationary vacuum space–times with whole cylinder symmetry</title><author>Eriş, Ahmet ; Nutku, Yavuz</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c322t-b2d95dc10710f283eab8ec7ed776c9991d139fd2e616cd1b5bc36328f2e833093</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1975</creationdate><topic>CYLINDRICAL CONFIGURATION</topic><topic>EINSTEIN FIELD EQUATIONS- GRAVITATIONAL FIELDS</topic><topic>GENERAL RELATIVITY THEORY</topic><topic>HAMILTON-JACOBI EQUATIONS</topic><topic>METRICS</topic><topic>N76300 -Physics (Theoretical)-Gravitation & General Relativity</topic><topic>RIEMANN SPACE</topic><topic>SPACE-TIME</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Eriş, Ahmet</creatorcontrib><creatorcontrib>Nutku, Yavuz</creatorcontrib><creatorcontrib>Department of Physics, Middle East Technical University, Ankara, Turkey</creatorcontrib><collection>CrossRef</collection><collection>OSTI.GOV</collection><jtitle>J. 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In this approach the emphasis is on a correspondence between the solution of the Einstein field equations and the geodesics in an appropriate Riemannian configuration space. Using Hamilton–Jacobi techniques, we obtain the geodesics and construct the resulting space–time geometries. We find that the light cone structure of the configuration space delineates the distinct exterior fields of Lewis and van Stockum which together form the most general solution with whole cylinder symmetry.</abstract><cop>United States</cop><doi>10.1063/1.522689</doi><tpages>4</tpages></addata></record>
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subjects	CYLINDRICAL CONFIGURATION EINSTEIN FIELD EQUATIONS- GRAVITATIONAL FIELDS GENERAL RELATIVITY THEORY HAMILTON-JACOBI EQUATIONS METRICS N76300 -Physics (Theoretical)-Gravitation & General Relativity RIEMANN SPACE SPACE-TIME
title	Harmonic mappings of Riemannian manifolds and stationary vacuum space–times with whole cylinder symmetry
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