Conformally symmetric vacuum solutions of the gravitational field equations in the brane-world models

TL;DR

This paper derives exact non-static vacuum solutions in brane-world gravity using conformal symmetry, analyzing their physical implications and potential to explain galactic rotation curves without dark matter.

Contribution

It introduces a new class of solutions with conformal symmetry in brane-world models, linking geometric properties to galactic dynamics and dark matter alternatives.

Findings

Solutions exhibit monotonically increasing tangential velocity tending to a constant at large distances.

Dark radiation and pressure behaviors are characterized and related to the solutions.

Potential explanation for galactic rotation curves without dark matter.

Abstract

A class of exact solutions of the gravitational field equations in the vacuum on the brane are obtained by assuming the existence of a conformal Killing vector field, with non-static and non-central symmetry. In this case the general solution of the field equations can be obtained in a parametric form in terms of the Bessel functions. The behavior of the basic physical parameters describing the non-local effects generated by the gravitational field of the bulk (dark radiation and dark pressure) is also considered in detail, and the equation of state satisfied at infinity by these quantities is derived. As a physical application of the obtained solutions we consider the behavior of the angular velocity of a test particle moving in a stable circular orbit. The tangential velocity of the particle is a monotonically increasing function of the radial distance and, in the limit of large values of the radial coordinate, tends to a constant value, which is independent on the parameters describing the model. Therefore a brane geometry admitting a one-parameter group of conformal motions may provide an explanation for the dynamics of the neutral hydrogen clouds at large distances from the galactic center, which is usually explained by postulating the existence of the dark matter.