  Let X be a strictly pseudoconcave domain in a closed polarized complex
manifold (Y,L) where L is a (semi-)positive line bundle over Y. Any given
Hermitian metric on L, together with a volume form, induces by restriction to X
a Hilbert space structure on the space of global holomorphic sections on Y with
values in the k:th tensor power of L. In this paper the leading large k
asymptotics for the corresponding Bergman kernels and metrics are obtained in
terms of the curvature of L and of the boundary of X (undere a certain
compatibility assumption). The convergence of the Bergman metrics is obtained
in a very general setting where X is replaced by a compact subset. As an
application the (generalized) equilibrium measure of the polarized
pseudoconcave domain X is computed explicitely. Applications to the zero and
mass distribution of random holomorphic sections and the eigenvaluedistribution
of Toeplitz operators will appear elsewhere.
