All the solutions of the form M2 × W σd - 2 for Lovelock gravity in vacuum in the Chern-Simons case

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In this paper we classify a certain family of solutions of Lovelock gravity in the Chern-Simons (CS) case, in arbitrary (odd) dimension, d ≥ 5. The spacetime is characterized by admitting a metric that is a warped product of a two-dimensional spacetime M2 and an (a priori) arbitrary Euclidean manifo...

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Autor principal: Oliva, J.
Formato: Artículo publishedVersion
Lenguaje:Inglés
Publicado: 2013
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00222488_v54_n4_p_Oliva
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paperaa:paper_00222488_v54_n4_p_Oliva2023-06-12T16:44:38Z All the solutions of the form M2 × W σd - 2 for Lovelock gravity in vacuum in the Chern-Simons case J. Math. Phys. 2013;54(4) Oliva, J. In this paper we classify a certain family of solutions of Lovelock gravity in the Chern-Simons (CS) case, in arbitrary (odd) dimension, d ≥ 5. The spacetime is characterized by admitting a metric that is a warped product of a two-dimensional spacetime M2 and an (a priori) arbitrary Euclidean manifold σd-2 of dimension d - 2. We show that the solutions are naturally classified in terms of the equations that restrict σd-2. According to the strength of such constraints we found the following branches in which σd-2 has to fulfill: a Lovelock equation with a single vacuum (Euclidean Lovelock Chern-Simons in dimension d - 2), a single scalar equation that is the trace of an Euclidean Lovelock CS equation in dimension d - 2, or finally a degenerate case in which σd-2 is not restricted at all. We show that all the cases have some degeneracy in the sense that the metric functions are not completely fixed by the field equations. This result extends the static five-dimensional case previously discussed in Dotti et al. [Phys. Rev. D76, 064038 (2007)]10.1103/PhysRevD.76.064038, and it shows that in the CS case, the inclusion of higher powers in the curvature does not introduce new branches of solutions in Lovelock gravity. Finally, we comment on how the inclusion of a non-vanishing torsion may modify this analysis. © 2013 American Institute of Physics. 2013 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00222488_v54_n4_p_Oliva
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
language Inglés
orig_language_str_mv eng
description In this paper we classify a certain family of solutions of Lovelock gravity in the Chern-Simons (CS) case, in arbitrary (odd) dimension, d ≥ 5. The spacetime is characterized by admitting a metric that is a warped product of a two-dimensional spacetime M2 and an (a priori) arbitrary Euclidean manifold σd-2 of dimension d - 2. We show that the solutions are naturally classified in terms of the equations that restrict σd-2. According to the strength of such constraints we found the following branches in which σd-2 has to fulfill: a Lovelock equation with a single vacuum (Euclidean Lovelock Chern-Simons in dimension d - 2), a single scalar equation that is the trace of an Euclidean Lovelock CS equation in dimension d - 2, or finally a degenerate case in which σd-2 is not restricted at all. We show that all the cases have some degeneracy in the sense that the metric functions are not completely fixed by the field equations. This result extends the static five-dimensional case previously discussed in Dotti et al. [Phys. Rev. D76, 064038 (2007)]10.1103/PhysRevD.76.064038, and it shows that in the CS case, the inclusion of higher powers in the curvature does not introduce new branches of solutions in Lovelock gravity. Finally, we comment on how the inclusion of a non-vanishing torsion may modify this analysis. © 2013 American Institute of Physics.
format Artículo
Artículo
publishedVersion
author Oliva, J.
spellingShingle Oliva, J.
All the solutions of the form M2 × W σd - 2 for Lovelock gravity in vacuum in the Chern-Simons case
author_facet Oliva, J.
author_sort Oliva, J.
title All the solutions of the form M2 × W σd - 2 for Lovelock gravity in vacuum in the Chern-Simons case
title_short All the solutions of the form M2 × W σd - 2 for Lovelock gravity in vacuum in the Chern-Simons case
title_full All the solutions of the form M2 × W σd - 2 for Lovelock gravity in vacuum in the Chern-Simons case
title_fullStr All the solutions of the form M2 × W σd - 2 for Lovelock gravity in vacuum in the Chern-Simons case
title_full_unstemmed All the solutions of the form M2 × W σd - 2 for Lovelock gravity in vacuum in the Chern-Simons case
title_sort all the solutions of the form m2 × w σd - 2 for lovelock gravity in vacuum in the chern-simons case
publishDate 2013
url http://hdl.handle.net/20.500.12110/paper_00222488_v54_n4_p_Oliva
work_keys_str_mv AT olivaj allthesolutionsoftheformm2wsd2forlovelockgravityinvacuuminthechernsimonscase
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