For a negative cosmological constant Λ, C-metric with acceleration parameter smaller than the critical value, a<1/lΛ, (where lΛ2=–3/Λ) describes an accelerated black hole in asymptotically anti-de Sitter spacetime.
Three-dimensional diagrams on the following pages represent a causal structure of the C-metric universe outside of the black hole. Angular coordinate φ around the axis of motion is suppressed (a rotation around this axis is a symmetry of the spacetime).
The boundary of the diagram corresponds to the conformal infinity. Horizon of the black holes is indicated by a dark surface. It is a null surfaces and thus it is only one way traversable for a physical observer.
In one set of diagrams, the black hole horizon is depicted by two joined cone-like surfaces. It reflects the null character of the horizon with null generators running from the neck of the horizon to the infinity. An alternative set of diagrams represents the horizon by two joined drop-like surfaces. It suggests that the black hole is a localized object. This representation is more useful in a limit of a negligible mass when the black hole turns to a test particle.
Standard two-dimensional conformal diagrams for C-metric depict surfaces ξ,φ=constant. Embedding of these surfaces into the whole spacetime is also shown.
|black hole visualized with cone-like horizon||black hole visualized with drop-like horizon|
Interactive diagrams needs a browser supporting Java applets. It uses LiveGraphics3D by Martin Kraus. It can take some time to download and to initiate these diagrams.
© 2005-12-31; Pavel Krtouš <Pavel.Krtous@mff.cuni.cz>