V Pravda and A Pravdová 2001 Class. Quantum Grav. 18 1205 doi:10.1088/0264-9381/18/7/305
V Pravda and A Pravdová
Show affiliationsWith 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 (a) falling under the black hole horizon; (b) crossing the acceleration horizon; and (c) 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.
83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)
Issue 7 (7 April 2001)
Received 6 November 2000
V Pravda and A Pravdová 2001 Class. Quantum Grav. 18 1205
E G Adelberger 2001 Class. Quantum Grav. 18 2397
Yoshitaka Degura and Kiyoshi Shiraishi 2000 Class. Quantum Grav. 17 4031
U S Nilsson et al 2000 Class. Quantum Grav. 17 3119
Lior M Burko 2000 Class. Quantum Grav. 17 227
A de Vries 2000 Class. Quantum Grav. 17 123
Ron Donagi et al 2000 Class. Quantum Grav. 17 1049
Piotr T Chrusciel 1999 Class. Quantum Grav. 16 689
Jorge L Cervantes-Cota 1999 Class. Quantum Grav. 16 3903
Peter Hübner 1999 Class. Quantum Grav. 16 2823