  Regge-Teitelboim embedding gravity is the modified gravity based on a simple
string-inspired geometrical principle: our spacetime is considered here as a
4-dimensional surface in a flat bulk. This theory is similar to the recently
popular theory of mimetic gravity: the modification of gravity appears in both
theories as a result of the change of variables in the action of General
Relativity. Embedding gravity, as well as mimetic gravity, can be used in
explaining the dark matter mystery since, in both cases, the modified theory
can be presented as General Relativity with additional fictitious matter
(embedding matter or mimetic matter). For the general case, we obtain the
equations of motion of embedding matter in terms of embedding function as a set
of first-order dynamical equations and constraints consistent with them. Then
we construct a non-relativistic limit of these equations, in which the motion
of embedding matter turns out to be slow enough so that it can play the role of
cold dark matter. The non-relativistic 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.
