H. -J. Schmidt, D. Singleton
We present an exact solution to 2+1 dimensional gravity plus a self-interacting real scalar field. The spatial part of the metric of the solution is flat but the temporal part behaves like asymptotic Anti-de Sitter space-time. The scalar field has logarithmic behavior as one would expect for a massless scalar field in flat space-time. The metric of the solution has no horizons and is thus not a black hole space-time. The solution can be most closely likened to gravitating scalar field solutions in 3+1 dimensions but with certain oddities connected with the 2+1 dimensional character of the space-time. One such odd feature is that the energy density is zero. The space-time is curved entirely due to a non-zero radial pressure. The present solution is unique to 2+1 dimensions; it does not carry over to 3+1 dimensions.
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http://arxiv.org/abs/1212.1285
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