AdS spacetimes and isometric embeddings

2013/02/07 by Steven Willison, Willison, Steven
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Noncommutative and Quantum Gravity Theories

paper · pdf · doi:10.48550/arxiv.1302.1762

openalex publication_date 2013/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An algebraic global isometric embedding of the nonrotating BTZ black hole is presented. The ambient spacetime is \mathbbM^2,3, the 3+2 dimensional flat spacetime. We also present the analogous embedding for the Euclidean BTZ spacetime and by performing a kind of double analytic continuation construct a 1-parameter family of embeddings of cosmological AdS spacetime into \mathbbM^2,3 which coincide asymptotically with the embedded BTZ manifold of the appropriate mass. Finally we note that the family of embeddings of cosmological AdS_n into \mathbbM^2,n generalises to higher dimensions.

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