Form invariance of differential equations in general relativity
Einstein equations for several matter sources in Robertson-Walker and Bianchi I type metrics, are shown to reduce to a kind of second-order nonlinear ordinary differential equation ÿ + αf(y)ẏ + βf(y)(Latin small letter esh)f(y)dy + γf(y) = 0. Also, it appears in the generalized statistical mechanics...
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| Formato: | Artículo publishedVersion |
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1997
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00222488_v38_n5_p2565_Chimento https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00222488_v38_n5_p2565_Chimento_oai |
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| Sumario: | Einstein equations for several matter sources in Robertson-Walker and Bianchi I type metrics, are shown to reduce to a kind of second-order nonlinear ordinary differential equation ÿ + αf(y)ẏ + βf(y)(Latin small letter esh)f(y)dy + γf(y) = 0. Also, it appears in the generalized statistical mechanics for the most interesting value q = -1. The invariant form of this equation is imposed and the corresponding nonlocal transformation is obtained. The linearization of that equation for any α, β, and γ is presented and for the important case f = byn + k with β = α2 (n + 1)/(n + 2)2 its explicit general solution is found. Moreover, the form invariance is applied to yield exact solutions of some other differential equations. © 1997 American Institute of Physics. |
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