Uniformly accelerating black holes in a de Sitter universe

Abstract

A class of exact solutions of Einstein's equations is analysed which describes uniformly accelerating charged black holes in an asymptotically de Sitter universe. This is a generalisation of the C-metric which includes a cosmological constant. The physical interpretation of the solutions is facilitated by the introduction of a new coordinate system for de Sitter space which is adapted to accelerating observers in this background. The solutions considered reduce to this form of the de Sitter metric when the mass and charge of the black holes vanish.Comment: 6 pages REVTeX, 3 figures, to appear in Phys. Rev. D. Figure 2 correcte

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“…This is completely different from the situation in the de Sitter universe, in which case the acceleration A of analogous observers may be unbounded, see e.g. [23], [25], [26]. Note that such infinite acceleration corresponds to (null) observers in the de Siter universe which move along the cosmological horizon.…”

“…Although this is a simple extension of our previous results presented in [25], we shall demonstrate that there are some interesting new features and fundamental differences from the analogous de Sitter case.…”

“…Only the first steps have been done. Using a suitable coordinate system adapted to the motion of uniformly accelerating particles in de Sitter space the physical meaning of the parameters appearing in solutions [18] could be determined [25]. On the other hand, the most recent paper by Bičák and Krtouš [26] on accelerated test sources in de Sitter spacetime may be of a great help for understanding the global structure of these solutions.…”

“…It may be seen that, either when A = 0 or when both m = 0 and e = 0, we obtain ζ(θ) = − cos θ so that G(θ) = sin θ. Otherwise these can be expressed in terms of Jacobian elliptic functions [25]. It is obvious that for A = 0, c = 1 the metric (14) exactly reduces to the familiar form of the Reissner-Nordstrøm-anti-de Sitter black hole solution in which the parameters m and e have the usual interpretation and the curvature singularity is located at r = 0.…”

“…This analogue of the accelerated coordinates for the de Sitter spacetime [25] is given by the following parameterisation of the hyperboloid (1),…”