Non-existence of Asymptotically Flat Geons in 2+1 Gravity
arXiv:0809.3022 · doi:10.1088/0264-9381/26/7/075012
Abstract
Geons, small topological structures that exhibit particle properties such as charge and angular momentum without the presence of matter sources, have been extensively discussed in 3+1-dimensional general relativity. Given the recent renewal of interest in 2+1 gravity, it is natural to ask whether or not the notion of geons extends to three dimensions. We prove here that, in contrast to the 3+1-dimensional case, there are no 2+1-dimensional asymptotically flat solutions of the vacuum Einstein or Einstein-Maxwell equations containing geons. In contrast, 2+1-dimensional asymptotically anti-de Sitter spacetimes can indeed contain geons; however, the geons are always hidden behind a single black hole horizon. We also prove sufficient conditions for the non-existence of 2+1-dimensional asymptotically flat geon-containing solutions.
22 pages. Typos fixed. Clarified proof of Corollary 2 provided. Discussion of applicability to other theories of 2+1 gravity, including topologically massive gravity added to conclusion