2000/10/26 by V. Pravda, Vojtěch Pravda, A. Pravdova +1 · 3 citations
Physics and Astronomy · #Acceleration #Black Holes and Theoretical Physics #Circular symmetry #Classical mechanics #Cosmology and Gravitation Theories #Geometry #Gravitational singularity #Mathematical physics #Metric (unit) #Physics #Quantum mechanics #Relativity and Gravitational Theory #Symmetry (geometry) #gr-qc
paper · pdf · doi:10.1088/0264-9381/18/7/305
published as Class.Quant.Grav.18:1205-1216,2001 · 10 pages, 12 EPS figures, changes mainly in abstract & introduction
arxiv created 2000/10/26 · openalex publication_date 2001/03/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 (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.