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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 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.


Documento: Artículo
Título:All the solutions of the form M2 × W σd - 2 for Lovelock gravity in vacuum in the Chern-Simons case
Autor:Oliva, J.
Filiación:Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Valdivia, Chile
Universidad de Buenos Aires, FCEN-UBA, Ciudad Universitaria, Pabellón I, 1428 Buenos Aires, Argentina
Título revista:Journal of Mathematical Physics
Título revista abreviado:J. Math. Phys.


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---------- APA ----------
(2013) . All the solutions of the form M2 × W σd - 2 for Lovelock gravity in vacuum in the Chern-Simons case. Journal of Mathematical Physics, 54(4).
---------- CHICAGO ----------
Oliva, J. "All the solutions of the form M2 × W σd - 2 for Lovelock gravity in vacuum in the Chern-Simons case" . Journal of Mathematical Physics 54, no. 4 (2013).
---------- MLA ----------
Oliva, J. "All the solutions of the form M2 × W σd - 2 for Lovelock gravity in vacuum in the Chern-Simons case" . Journal of Mathematical Physics, vol. 54, no. 4, 2013.
---------- VANCOUVER ----------
Oliva, J. 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).