Weak field limit for embedding gravity

TL;DR

This paper develops a perturbation theory for embedding gravity in a flat background, deriving a nonlinear equation to model gravitational potential, which can replicate dark matter effects in galactic halos.

Contribution

It introduces a linear perturbation approach for embedding gravity and derives a nonlinear differential equation to model gravitational potential in a spherically symmetric setting.

Findings

Derived a nonlinear differential equation for gravitational potential.

Proposed a background embedding function matching galactic dark matter distribution.

Showed the model's potential to explain dark matter effects in galaxies.

Abstract

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.