Possible types of dark matter condensation in embedding gravity
S. A. Paston, A. J. Ziyatdinov
TL;DR
This work proposes embedding gravity (Regge-Teitelboim gravity) as a fundamental modification of general relativity, which introduces fictitious matter of embedding gravity (FMEG) that can move independently of ordinary matter. In the weak-field, unfolded-embedding limit, FMEG behaves like cold dark matter with a linear stress–density relation $\tau^{ik}= w^{ik}\rho_\tau$, and its total density is bounded by $\rho_b=1/(4\pi G L^2)$, suppressing DM-like effects on small scales. The paper classifies possible static FMEG condensations in the linear regime into wall-type, thick-string-type, and, in the isotropic case where all eigenvalues coincide, spherical isothermal condensations that yield $\rho_\tau\propto 1/r^2$ at large radii and flat rotation curves with $v_* = \sqrt{2w}$, resembling observed galactic halos and the ISO profile. The results suggest DM can arise from gravitational degrees of freedom in embedding gravity, potentially connecting DM phenomenology to the geometry of spacetime embedding, with future work needed to couple to cosmic expansion and large-scale structure.
Abstract
We investigate the possibility of explaining the observed effects usually attributed to the existence of dark matter through a transition from GR to a modified theory of gravity - embedding gravity. Since this theory can be reformulated as GR with additional fictitious matter of embedding gravity (FMEG), which moves independently of ordinary matter, we analyse solutions in which FMEG behaves similarly to cold dark matter. An upper bound on the possible density of FMEG is obtained, which explains the absence of dark matter effects on small scales. Possible static condensed structures of FMEG are found, which can be reduced to configurations of the types wall, string, and sphere. In the latter case, FMEG exhibits the properties of an isothermal ideal gas which has a linear equation of state. The emerging spherical condensations of FMEG create potential wells that facilitate galaxy formation. For large values of the radius, the corresponding density distribution profile behaves in the same way as the pseudo-isothermal profile (ISO), which is successfully employed in fitting galactic dark halo regions, and provides flat galactic rotation curves.