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Weak field limit for embedding gravity

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arxiv 2210.13272 v2 pith:GY3Y3USZ submitted 2022-10-24 gr-qc

S.S. Kuptsov , M.V. Ioffe , S.N. Manida , S.A. Paston This is my paper · ORCID
classification gr-qc
keywords embeddingbackgroundfunctioncorrectionsequationsfieldgravitationalgravity
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We study a perturbation theory for embedding gravity equations in a background for which corrections to the embedding function are linear with respect to corrections to the flat metric. The arbitrariness remaining after solving the linearized field equations is fixed by an assumption that the solution is static in the second order. A nonlinear differential equation is obtained, which makes it possible to find the gravitational potential for a spherically symmetric case if a background embedding is given. An explicit form of a spherically symmetric background parameterized by one function of radius is proposed. It is shown that this function can be chosen in such a way that the gravitational potential is in a good agreement with the observed distribution of dark matter in a galactic halo.

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  1. Classification of ten-dimensional embeddings of spherically symmetric static metrics

    gr-qc 2024-11 conditional novelty 6.0 of 10

    The authors enumerate the 52 classes of SO(3)xT1-symmetric embeddings of static spherical metrics into (1,9)-dimensional flat space and assess unfolding and the existence of smooth Minkowski embeddings.

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