Boundary regularity, uniqueness and nonuniqueness for AH Einstein metrics on 4-manifolds

摘要

This paper studies several aspects of asymptotically hyperbolic (AH) Einstein metrics, mostly on 4-manifolds. We prove boundary regularity (at infinity) for such metrics and establish uniqueness under natural conditions on the boundary data. By examination of explicit black hole metrics, it is shown that neither uniqueness nor finiteness holds in general for AH Einstein metrics with a prescribed conformal infinity. We then describe natural conditions which are sufficient to ensure finiteness. (C) 2002 Elsevier Science (USA). All rights reserved. [References: 39]