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

Michael T. Anderson

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arXiv · math/0104171

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

Michael T. Anderson

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Abstract

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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BibTeX RIS

Michael T. Anderson. 2002-06-11. Boundary regularity, uniqueness and non-uniqueness for AH Einstein metrics on 4-manifolds. https://arxiv.org/abs/math/0104171

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