We propose Lobachevsky boundary conditions that lead to asymptotically H^2xR
solutions. As an example we check their consistency in conformal Chern-Simons
gravity. The canonical charges are quadratic in the fields, but nonetheless
integrable, conserved and finite. The asymptotic symmetry algebra consists of
one copy of the Virasoro algebra with central charge c=24k, where k is the
Chern-Simons level, and an affine u(1). We find also regular non-perturbative
states and show that none of them corresponds to black hole solutions. We
attempt to calculate the one-loop partition function, find a remarkable
separation between bulk and boundary modes, but conclude that the one-loop
partition function is ill-defined due to an infinite degeneracy. We comment on
the most likely resolution of this degeneracy.Comment: 24 pp, v2: expanded footnote 1; added Killing vectors (2.8), (2.9);
added subsection 5.4 on Lobachevsky/field theory ma
