We consider solutions with conformal symmetry of the static, spherically symmetric gravitational field equations in the vacuum in the brane world scenario. By assuming that the vector field generating the symmetry is nonstatic, the general solution of the field equations on the brane can be obtained in an exact parametric form, with the conformal factor taken as parameter. 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. In this case the tangential velocity can be expressed as a function of the conformal factor and some integration constants only. For a specific range of integration constants, the tangential velocity of the test particle tends, in the limit of large radial distances, to a constant value. This behavior is specific to galactic rotation curves and is explained usually by invoking the hypothesis of dark matter. The limiting value of the angular velocity of the test particle can be obtained as a function of the baryonic mass and radius of the galaxy. The behavior of the dark radiation and dark pressure terms is also considered in detail, and it is shown that they can be expressed in terms of the rotational velocity of a test particle. Hence all the predictions of the present model can be tested observationally. Therefore the existence of the nonlocal effects, generated by the free gravitational field of the bulk in a conformally symmetric brane, may provide an explanation for the dynamics of the neutral hydrogen clouds at large distances from the galactic center.

• Received 19 February 2004

DOI:https://doi.org/10.1103/PhysRevD.70.024010