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

2001/04/17 by Michael T. Anderson, Anderson, Michael T. · 6 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #math.DG

paper · pdf · doi:10.48550/arxiv.math/0104171

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

openalex publication_date 2001/04/17 · arxiv created 2002/06/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Thermodynamics of black holes in anti-de Sitter space

Cited by

• Maskit combinations of Poincare-Einstein metrics
• Poincaré-Einstein 4-manifolds with conformally Kähler geometry
• On the Poincaré-Einstein manifolds with cylindrical conformal infinity
• Harmonic maps and the topology of conformally compact Einstein manifolds
• Poincare-Einstein metrics and the Schouten tensor
• On the Parallels Between Minimal Surfaces and Einstein Four-Manifolds

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