Co-accelerated particles in the C-metric

TL;DR

This paper analyzes geodesics in the C-metric, revealing conditions for stable particle orbits around accelerating black holes and providing analytical solutions for special cases.

Contribution

It characterizes the types of geodesics in the C-metric and identifies conditions for stability of particle orbits, including analytical solutions for special geodesics.

Findings

Existence of stable timelike geodesics when mA is below a critical value

Null geodesics of the third type are always unstable

Analytical forms for special geodesics are derived

Abstract

With appropriately chosen parameters, the C-metric represents two uniformly accelerated black holes moving in the opposite directions on the axis of the axial symmetry (the z-axis). The acceleration is caused by nodal singularities located on the z-axis. In the~present paper, geodesics in the~C-metric are examined. In general there exist three types of timelike or null geodesics in the C-metric: geodesics describing particles 1) falling under the black hole horizon; 2)crossing the acceleration horizon; and 3) orbiting around the z-axis and co-accelerating with the black holes. Using an effective potential, it can be shown that there exist stable timelike geodesics of the third type if the product of the parameters of the C-metric, mA, is smaller than a certain critical value. Null geodesics of the third type are always unstable. Special timelike and null geodesics of the third type are also found in an analytical form.