arXiv subjects

A. J. Ziyatdinov

Publications and source records attributed to A. J. Ziyatdinov.

2 recordsLinked to original sources

arXiv2026

Analysis of the equations of motion of fictitious matter in embedding theory

Embedding theory is a possible modification of general relativity that provides a framework for explaining the observed effects typically attributed to dark matter. The idea of this modification is to consider our spacetime as a four-dimensional surface in a ten-dimensional flat ambient space. The equations of motion in embedding theory can be reformulated as a set of Einstein equations with the contribution of some additional fictitious matter and of equations describing this matter. We analyze static solutions of these equations, which are reduced to fictitious-matter configurations of the wall, string, and ball types. The string case is ultimately described by the Liouville equation, and the ball case is described by its three dimensional analogue. For the string case, we show that as the density contribution decreases at infinity, all solutions to the Liouville equation are rotationally symmetric. For the case of the ball, we show that under the assumption of spherical symmetry, there exists a unique one-parameter family of solutions that are smooth at the center.

gr-qc↗

arXiv2026

Possible types of dark matter condensation in embedding gravity

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.

gr-qc↗