All the solutions of the form M2 × W σd - 2 for Lovelock gravity in vacuum in the Chern-Simons case
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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2013
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00222488_v54_n4_p_Oliva https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00222488_v54_n4_p_Oliva_oai |
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I28-R145-paper_00222488_v54_n4_p_Oliva_oai2024-08-16 Oliva, J. 2013 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. application/pdf http://hdl.handle.net/20.500.12110/paper_00222488_v54_n4_p_Oliva info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar J. Math. Phys. 2013;54(4) All the solutions of the form M2 × W σd - 2 for Lovelock gravity in vacuum in the Chern-Simons case info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00222488_v54_n4_p_Oliva_oai |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-145 |
| collection |
Repositorio Digital de la Universidad de Buenos Aires (UBA) |
| 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 https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00222488_v54_n4_p_Oliva_oai |
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AT olivaj allthesolutionsoftheformm2wsd2forlovelockgravityinvacuuminthechernsimonscase |
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1809356793407602688 |