Explicit mixed-monodromy Liouville solutions are constructed and their large-hyperbolic limits are used to describe time-symmetric slices of 2+1 gravity with particles and black holes.
Explicit solutions for Point Particles and Black Holes in spaces of constant curvature in 2+1-D Gravity
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In this paper we consider space-times containing matter expanding or contracting according to a time-dependent scale factor. Cosmologies with vanishing, positive or negative cosmological constant are considered. In the case of vanishing or negative cosmological constant open and closed spatial surfaces are solutions while in the case of positive cosmological constant only closed surfaces exist. The gravitational field is solved explicitly in the case of 1 or 2 particles, 1 black-hole, and 1 black-hole vacuum state.
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Mixed Solutions to the Liouville Equation
Explicit mixed-monodromy Liouville solutions are constructed and their large-hyperbolic limits are used to describe time-symmetric slices of 2+1 gravity with particles and black holes.