Speaker
Description
Certain observed phenomena cannot be explained within the framework of General Relativity (GR) without the introduction of dark matter. One may attempt to avoid its introduction by moving to a modified theory of gravity—embedding gravity. Within this framework, a 4-dimensional spacetime is considered as a surface embedded in a 10-dimensional flat Minkowski space.
It turns out that it is possible to reformulate embedding gravity in such a way that a certain contribution, describing the fictitious matter of embedded gravity (FMEG), is added to the GR action. The equations of motion describing this matter prove to be excessively complex; therefore, to simplify the analysis, we employ the idea of expanding the embedding function into a Taylor series up to the quadratic contribution on a certain scale.
Static condensations of FMEG arise only for values of the matter density (both ordinary and fictitious) that are below a certain critical value. Among the found static configurations, a "string" emerges—a solution for which the density function is independent of one of the coordinates. It is known from the mathematical literature that such a solution is the only one possible (and, moreover, radially symmetric), provided that the integral of the density over the plane transverse to the string converges. This assertion can be strengthened: it turns out to be sufficient to require a simple decrease of the density function in the transverse directions. This refinement may be important since the convergence of the density integral does not always occur in physical situations. For example, for another found static configuration, a "ball", this integral diverges; and it is precisely such a slow decrease of the matter density in the dark halos of galaxies that provides the observed flatness of their rotation curves.
