The approach to gravity as a theory of embedded surface
A. A. Sheykin, S. A. Paston
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LaTeX, 10 pages. Proceedings of "II Russian-Spanish Congress Particle and Nuclear Physics at all Scales and Cosmology", Saint-Petersburg, October 1-4, 2013
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.
Karmarkar-Tolman Embedded Charged Anisotropic Stars in f(R) Gravity
School of Physics and Electronics, Hunan University（湖南大学物理与电子学院）；Institute of Physics, Gomal University（戈尔姆大学物理研究所）；Hunan Provincial Key Laboratory of High-Energy Scale Physics and Applications, Hunan University（湖南大学高能标物理与应用湖南省重点实验室）
