Abstract
In this paper I show that one can have asymptotically de Sitter, anti-de Sitter (AdS), and flat solutions in Gauss-Bonnet gravity without a cosmological constant term in field equations. First, I introduce static solutions whose three surfaces at fixed and have constant positive (), negative (), or zero () curvature. I show that for one can have asymptotically de Sitter, AdS, and flat spacetimes, while for the case of , one has only asymptotically AdS solutions. Some of these solutions present naked singularities, while some others are black hole or topological black hole solutions. I also find that the geometrical mass of these five-dimensional spacetimes is , which is different from the geometrical mass of the solutions of Einstein gravity. This feature occurs only for the five-dimensional solutions, and is not repeated for the solutions of Gauss-Bonnet gravity in higher dimensions. Second, I add angular momentum to the static solutions with , and introduce the asymptotically AdS charged rotating solutions of Gauss-Bonnet gravity. Finally, I introduce a class of solutions which yields an asymptotically AdS spacetime with a longitudinal magnetic field, which presents a naked singularity, and generalize it to the case of magnetic rotating solutions with two rotation parameters.
- Received 29 May 2004
DOI:https://doi.org/10.1103/PhysRevD.70.064019
©2004 American Physical Society