For a negative cosmological constant Λ, C-metric with acceleration parameter smaller than the critical value, `a`<1/`l`_{Λ}, (where `l`_{Λ}^{2}=–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>`