2 research outputs found
Nariai, Bertotti-Robinson and anti-Nariai solutions in higher dimensions
We find all the higher dimensional solutions of the Einstein-Maxwell theory
that are the topological product of two manifolds of constant curvature. These
solutions include the higher dimensional Nariai, Bertotti-Robinson and
anti-Nariai solutions, and the anti-de Sitter Bertotti-Robinson solutions with
toroidal and hyperbolic topology (Plebanski-Hacyan solutions). We give explicit
results for any dimension D>3. These solutions are generated from the
appropriate extremal limits of the higher dimensional near-extreme black holes
in a de Sitter, and anti-de Sitter backgrounds. Thus, we also find the mass and
the charge parameters of the higher dimensional extreme black holes as a
function of the radius of the degenerate horizon.Comment: 10 pages, 11 figures, RevTeX4. References added. Published versio
The extremal limits of the C-metric: Nariai, Bertotti-Robinson and anti-Nariai C-metrics
In two previous papers we have analyzed the C-metric in a background with a
cosmological constant, namely the de Sitter (dS) C-metric, and the anti-de
Sitter (AdS) C-metric, following the work of Kinnersley and Walker for the flat
C-metric. These exact solutions describe a pair of accelerated black holes in
the flat or cosmological constant background, with the acceleration A being
provided by a strut in-between that pushes away the two black holes. In this
paper we analyze the extremal limits of the C-metric in a background with
generic cosmological constant. We follow a procedure first introduced by
Ginsparg and Perry in which the Nariai solution, a spacetime which is the
direct topological product of the 2-dimensional dS and a 2-sphere, is generated
from the four-dimensional dS-Schwarzschild solution by taking an appropriate
limit, where the black hole event horizon approaches the cosmological horizon.
Similarly, one can generate the Bertotti-Robinson metric from the
Reissner-Nordstrom metric by taking the limit of the Cauchy horizon going into
the event horizon of the black hole, as well as the anti-Nariai by taking an
appropriate solution and limit. Using these methods we generate the C-metric
counterparts of the Nariai, Bertotti-Robinson and anti-Nariai solutions, among
others. One expects that the solutions found in this paper are unstable and
decay into a slightly non-extreme black hole pair accelerated by a strut or by
strings. Moreover, the Euclidean version of these solutions mediate the quantum
process of black hole pair creation, that accompanies the decay of the dS and
AdS spaces