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

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

2001-04-17

arxiv.org/abs/math/0104171v2

Mathematics

Differential Geometry

33pp, gap in one proof fixed, exposition improved. To appear in Advances in Math

Scientific paper

This paper studies several aspects of asymptotically hyperbolic 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.

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