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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todo:paper_00222488_v38_n5_p2565_Chimento2023-10-03T14:29:41Z Form invariance of differential equations in general relativity Chimento, L.P. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00222488_v38_n5_p2565_Chimento |
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Universidad de Buenos Aires |
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I-28 |
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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. |
| format |
JOUR |
| author |
Chimento, L.P. |
| spellingShingle |
Chimento, L.P. Form invariance of differential equations in general relativity |
| author_facet |
Chimento, L.P. |
| author_sort |
Chimento, L.P. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_00222488_v38_n5_p2565_Chimento |
| work_keys_str_mv |
AT chimentolp forminvarianceofdifferentialequationsingeneralrelativity |
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1782030697658056704 |