2014/01/01 by A. A. Sheykin, S. A. Paston
Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #gr-qc
paper · pdf · doi:10.1063/1.4891157
published as AIP Conference Proceedings 1606, 400 (2014) · LaTeX, 10 pages. Proceedings of "II Russian-Spanish Congress Particle and Nuclear Physics at all Scales and Cosmology", Saint-Petersburg, October 1-4, 2013
openalex publication_date 2014/01/01 · arxiv created 2014/02/05 · arxiv updated 2014/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
We study the approach to gravity in which our curved spacetime is considered as a surface in a flat ambient space of higher dimension (the embedding theory). The dynamical variable in this theory is not a metric but an embedding function. The Euler-Lagrange equations for this theory (Regge-Teitelboim equations) are more general than the Einstein equations, and admit “extra solutions” which do not correspond to any Einsteinian metric. The Regge-Teitelboim equations can be explicitly analyzed for the solutions with high symmetry. We show that symmetric embeddings of a static spherically symmetric asymptotically flat metrics in a 6-dimensional ambient space do not admit extra solutions of the vacuum Regge-Teitelboim equations. Therefore in the embedding theory the solutions with such properties correspond to the exterior Schwarzchild metric.