Co-accelerated particles in the C-metric

Details Co-accelerated particles in the C-metric Co-accelerated particles in the C-metric

2000-10-13

arxiv.org/abs/gr-qc/0010051v2

Class.Quant.Grav.18:1205-1216,2001

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 pages, 12 EPS figures, changes mainly in abstract & introduction

Scientific paper

10.1088/0264-9381/18/7/305

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.

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