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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1997
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00222488_v38_n5_p2565_Chimento http://hdl.handle.net/20.500.12110/paper_00222488_v38_n5_p2565_Chimento |
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paper:paper_00222488_v38_n5_p2565_Chimento2023-06-08T14:48:11Z Form invariance of differential equations in general relativity Chimento, Luis Pascual 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. Fil:Chimento, L.P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 1997 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00222488_v38_n5_p2565_Chimento http://hdl.handle.net/20.500.12110/paper_00222488_v38_n5_p2565_Chimento |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| description |
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. |
| author |
Chimento, Luis Pascual |
| spellingShingle |
Chimento, Luis Pascual Form invariance of differential equations in general relativity |
| author_facet |
Chimento, Luis Pascual |
| author_sort |
Chimento, Luis Pascual |
| title |
Form invariance of differential equations in general relativity |
| title_short |
Form invariance of differential equations in general relativity |
| title_full |
Form invariance of differential equations in general relativity |
| title_fullStr |
Form invariance of differential equations in general relativity |
| title_full_unstemmed |
Form invariance of differential equations in general relativity |
| title_sort |
form invariance of differential equations in general relativity |
| publishDate |
1997 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00222488_v38_n5_p2565_Chimento http://hdl.handle.net/20.500.12110/paper_00222488_v38_n5_p2565_Chimento |
| work_keys_str_mv |
AT chimentoluispascual forminvarianceofdifferentialequationsingeneralrelativity |
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1768541879126720512 |