Complete classification of spherically symmetric static space--times via Noether symmetries
Teoretičeskaâ i matematičeskaâ fizika, Tome 184 (2015) no. 1, pp. 92-105
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We provide a complete classification of spherically symmetric static space–times by their Noether symmetries. We obtain the determining equations for the Noether symmetries using the usual Lagrangian of a general spherically symmetric static space–time and integrate them in each considered case. In particular, we find that spherically symmetric static space–times are categorized into six distinct classes corresponding to the Noether algebras of dimensions $5$, $6$, $7$, $9$, $11$, and $17$. Using Noether`s theorem, we also find the first integrals corresponding to each symmetry. Moreover, we obtain some new spherically symmetric static solutions.
Keywords:
Noether symmetry, static space–time.
@article{TMF_2015_184_1_a5,
author = {F. Ali and T. Feroze and S. Ali},
title = {Complete classification of spherically symmetric static space--times via {Noether} symmetries},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {92--105},
publisher = {mathdoc},
volume = {184},
number = {1},
year = {2015},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2015_184_1_a5/}
}
TY - JOUR AU - F. Ali AU - T. Feroze AU - S. Ali TI - Complete classification of spherically symmetric static space--times via Noether symmetries JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2015 SP - 92 EP - 105 VL - 184 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2015_184_1_a5/ LA - ru ID - TMF_2015_184_1_a5 ER -
%0 Journal Article %A F. Ali %A T. Feroze %A S. Ali %T Complete classification of spherically symmetric static space--times via Noether symmetries %J Teoretičeskaâ i matematičeskaâ fizika %D 2015 %P 92-105 %V 184 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2015_184_1_a5/ %G ru %F TMF_2015_184_1_a5
F. Ali; T. Feroze; S. Ali. Complete classification of spherically symmetric static space--times via Noether symmetries. Teoretičeskaâ i matematičeskaâ fizika, Tome 184 (2015) no. 1, pp. 92-105. http://geodesic.mathdoc.fr/item/TMF_2015_184_1_a5/