Co-accelerated particles in the C-metric (Q2724838)

Geodesics are studied in the C-metric which represents two uniformly accelerated black-holes moving in opposite directions along the symmetry axis. The acceleration is caused by nodal singularities on the axis. In the static region free of curvature singularities, three types of timelike or null geodesics are identified, related to particles falling into the horizon of the black hole, particles crossing the acceleration horizon, and particles spinning around the axis and co-accelerating with the black holes. Whereas the null geodesics are unstable in the last case, timelike geodesics can be stable if the acceleration is below a critical value.