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Conformastatic spacetimes
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Conformastatic spacetimes : ウィキペディア英語版
Conformastatic spacetimes

Conformastatic spacetimes refer to a special class of static solutions to Einstein's equation in general relativity.
== Introduction ==

The line element for the conformastatic class of solutions in Weyl's canonical coordinates reads〔John Lighton Synge. ''Relativity: The General Theory'', Chapter VIII. Amsterdam: North-Holland Publishing Company (Interscience), 1960.〕〔Hans Stephani, Dietrich Kramer, Malcolm MacCallum, Cornelius Hoenselaers, Eduard Herlt . ''Exact Solutions of Einstein's Field Equations'' (2nd Edition), Chapter 18. Cambridge: Cambridge University Press, 2003.〕〔Guillermo A Gonzalez, Antonio C Gutierrez-Pineres, Paolo A Ospina. ''Finite axisymmetric charged dust disks in conformastatic spacetimes''. Physical Review D 78 (2008): 064058. (arXiv:0806.4285[gr-qc] )〕〔F D Lora-Clavijo, P A Ospina-Henao, J F Pedraza. ''Charged annular disks and Reissner–Nordström type black holes from extremal dust''. Physical Review D 82 (2010): 084005. (arXiv:1009.1005[gr-qc] )〕〔Ivan Booth, David Wenjie Tian. ''Some spacetimes containing non-rotating extremal isolated horizons''. Accepted by Classical and Quantum Gravity. (arXiv:1210.6889[gr-qc] )〕〔Antonio C Gutierrez-Pineres, Guillermo A Gonzalez, Hernando Quevedo. ''Conformastatic disk-haloes in Einstein-Maxwell gravity''. Physical Review D 87 (2013): 044010. (arXiv:1211.4941[gr-qc] )〕

(1)\qquad ds^2 = - e^ dt^2 + e^ \Big(d \rho^2 + d z^2 + \rho^2 d \phi^2 \Big)\;,

as a solution to the field equation

(2)\qquad R_-\fracRg_=8\pi T_\;.

Eq(1) has only one metric function \Psi(\rho,\phi,z) to be identified, and for each concrete \Psi(\rho,\phi,z), Eq(1) would yields a ''specific'' conformastatic spacetime.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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