Non-existence of Asymptotically Flat Geons in 2+1 Gravity
Kory A. Stevens, Kristin Schleich, Donald M. Witt
备注：
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
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.
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