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.
Spacetime Embedding Diagrams for Spherically Symmetric Black HolesGeneral Relativity and Gravitation
Citation InformationGiblin, J.T., Marolf, D. & Garvey, R. General Relativity and Gravitation (2004) 36: 83. doi:10.1023/B:GERG.0000006695.17232.2e