Galactic dark matter as a bulk effect on the brane

TL;DR

This paper explores how dark matter effects in galaxies can be explained by a brane world model, deriving exact solutions and observable predictions related to galactic rotation curves.

Contribution

It provides an exact analytic solution for vacuum gravitational fields on the brane with constant tangential velocity, linking dark radiation and dark pressure to observable galactic parameters.

Findings

Derived explicit form of bulk Weyl tensor projections on the brane.

Expressed physical quantities in terms of observable galactic parameters.

Provided a framework for testing brane world models with galactic rotation data.

Abstract

The behavior of the angular velocity of a test particle moving in a stable circular orbit in the vacuum on the brane is considered. In the brane world scenario, the four dimensional effective Einstein equation acquire extra terms, called dark radiation and dark pressure, respectively, which arise from the embedding of the 3-brane in the bulk. A large number of independent observations have shown that the rotational velocities of test particles gravitating around galaxies tend, as a function of the distance from the galactic center, toward constant values. By assuming a constant tangential velocity, the general solution of the vacuum gravitational field equations on the brane can be obtained in an exact analytic form. This allows us to obtain the explicit form of the projections of the bulk Weyl tensor on the brane, and the equation of state of the dark pressure as a function of the dark radiation. The physical and geometrical quantities are expressed in terms of observable/measurable parameters, like the tangential velocity, the baryonic mass and the radius of the galaxy. We also analyze the dynamics of test particles by using methods from the qualitative analysis of dynamical systems, by assuming a simple linear equation of state for the dark pressure. The obtained results provide a theoretical framework for the observational testing at the extra-galactic scale of the predictions of the brane world models.