For the two-dimensional Liouville equation arising in embedding theory, the authors prove that decay at infinity alone forces rotational symmetry, and for the three-dimensional case they prove uniqueness of smooth spherically symmetric solutions.
Dark matter from non-relativistic embedding gravity
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abstract
We study the possibility to explain the mystery of the dark matter through the transition from General Relativity to embedding gravity. This modification of gravity, which was proposed by Regge and Teitelboim, is based on a simple string-inspired geometrical principle: our spacetime is considered here as a 4-dimensional surface in a flat bulk. We show that among the solutions of embedding gravity, there is a class of solutions equivalent to solutions of GR with an additional contribution of non-relativistic embedding matter, which can serve as cold dark matter. We prove the stability of such type of solutions and obtain an explicit form of the equations of motion of embedding matter in the non-relativistic limit. According to them, embedding matter turns out to have a certain self-interaction, which could be useful in the context of solving the core-cusp problem that appears in the LambdaCDM model.
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Analysis of the equations of motion of fictitious matter in embedding theory
For the two-dimensional Liouville equation arising in embedding theory, the authors prove that decay at infinity alone forces rotational symmetry, and for the three-dimensional case they prove uniqueness of smooth spherically symmetric solutions.