Classics Illustrated: Limits of Spacetimes

Abstract

We carefully study the $e\to m$ and $e\to 0$ limits of the Reissner-Nordström spacetime using Geroch's definition of limits of spacetimes. This is implemented by embedding the one-parameter family of spacetimes in anti-de Sitter space, and as a result we obtain metrically correct Penrose diagrams. For $e\to m$ two distinct limits are studied.

arXiv comment23 pages, 13 figures

References in corpus (10)

• Isometric embeddings into the Minkowski space and new quasi-local mass
• Mapping Hawking into Unruh Thermal Properties
• Extremal limits and black hole entropy
• Towards Realistic String Vacua From Branes At Singularities
• A Spinning Anti-de Sitter Wormhole
• On limits of spacetimes -- a coordinate-free approach
• Spacetime Embedding Diagrams for Black Holes
• Isometric Embedding of BPS Branes in Flat Spaces with Two Times
• Spacetime Embedding Diagrams for Spherically Symmetric Black Holes
• Global Embedding of the Reissner-Nordström Metric in the Flat Ambient Space

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• The Tortoise and the Hare: A Causality Puzzle in AdS/CFT
• The $\Lambda$ to zero limit of spacetimes and its physical interpretation
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