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

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.

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

References in corpus (3)

• The Holographic Weyl anomaly
• Stress Tensors and Casimir Energies in the AdS/CFT Correspondence
• Nut Charge, Anti-de Sitter Space and Entropy

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