Acceleration, streamlines and potential flows in general relativity: analytical and numerical results

Analytical and numerical solutions for the integral curves of the velocity field (streamlines) of a steady-state flow of an ideal fluid with $p = \rho$ equation of state are presented. The streamlines associated with an accelerate black hole and a rigid sphere are studied in some detail, as well as, the velocity fields of a black hole and a rigid sphere in an external dipolar field (constant acceleration field). In the latter case the dipole field is produced by an axially symmetric halo or shell of matter. For each case the fluid density is studied using contour lines. We found that the presence of acceleration is detected by these contour lines. As far as we know this is the first time that the integral curves of the velocity field for accelerate objects and related spacetimes are studied in general relativity.