Abstract
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-Nordström 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 yield an embedding constant related to the surface gravity of the relevant horizon.
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Giblin, J.T., Marolf, D. & Garvey, R. Spacetime Embedding Diagrams for Spherically Symmetric Black Holes. General Relativity and Gravitation 36, 83–99 (2004). https://doi.org/10.1023/B:GERG.0000006695.17232.2e
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DOI: https://doi.org/10.1023/B:GERG.0000006695.17232.2e
- Black holes
- embedding diagram
- test particle