Spacetime Embedding Diagrams for Spherically Symmetric Black Holes

We show that it is possible to embed the 1+1 dimensional reduction of certain spherically symmetric black hole spacetimes into 2+1 Minkowski space. The spacetimes of interest (Schwarzschild de-Sitter, Schwarzschild anti de-Sitter, and Reissner-Nordstrom near the outer horizon) represent a class of m...

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Veröffentlicht in:arXiv.org 2003-06
Hauptverfasser: Giblin, John T, Marolf, Donald, Garvey, Robert H
Format: Artikel
Sprache:eng
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Zusammenfassung:We show that it is possible to embed the 1+1 dimensional reduction of certain spherically symmetric black hole spacetimes into 2+1 Minkowski space. The spacetimes of interest (Schwarzschild de-Sitter, Schwarzschild anti de-Sitter, and Reissner-Nordstrom near the outer horizon) represent a class of metrics whose geometries allow for such embeddings. The embedding diagrams have a dynamic character which allows one to represent the motion of test particles. We also analyze various features of the embedding construction, deriving the general conditions under which our procedure provides a smooth embedding. These conditions also yeild an embedding constant related to the surface gravity of the relevant horizon.
ISSN:2331-8422
DOI:10.48550/arxiv.0305102