Black Holes in a Compactified Spacetime

Abstract

We discuss properties of a 4-dimensional Schwarzschild black hole in a spacetime where one of the spatial dimensions is compactified. As a result of the compactification the event horizon of the black hole is distorted. We use Weyl coordinates to obtain the solution describing such a distorted black hole. This solution is a special case of the Israel-Khan metric. We study the properties of the compactified Schwarzschild black hole, and develop an approximation which allows one to find the size, shape, surface gravity and other characteristics of the distorted horizon with a very high accuracy in a simple analytical form. We also discuss possible instabilities of a black hole in the compactified space.

12 pages, 6 figures, RevTeX 3.1; references added

References in corpus (4)

• Static Axisymmetric Vacuum Solutions and Non-Uniform Black Strings
• Small localized black holes in a braneworld: Formulation and numerical method
• From Black Strings to Black Holes
• Initial Data for Black Holes and Black Strings in 5d

Cited by in corpus (24)

• The Phase Transition between Caged Black Holes and Black Strings - A Review
• Instabilities of Black Strings and Branes
• Small Black Holes on Cylinders
• New Phase Diagram for Black Holes and Strings on Cylinders
• Phase Structure of Black Holes and Strings on Cylinders
• Caged Black Holes: Black Holes in Compactified Spacetimes I -- Theory
• Violations of the Born rule in cool state-dependent horizons
• Black Holes in Higher-Dimensional Gravity
• Phases of Kaluza-Klein Black Holes: A Brief Review
• Interior of Distorted Black Holes
• Multi-black hole configurations on the cylinder
• Stationary Black Holes as Holographs
• Distorted Five-dimensional Electrically Charged Black Holes
• Distorted 5-dimensional vacuum black hole
• The Final State of Black Strings and p-Branes, and the Gregory-Laflamme Instability
• Stationary Black Holes as Holographs II
• Myers-Perry Black Hole in an External Gravitational Field
• Charged black holes in compactified spacetimes
• Supersymmetric Rotating Black Hole in a Compactified Spacetime
• A relativistic model of the topological acceleration effect
• A Distorted Black Ring
• Periodic analogues of the Kerr solutions: a numerical study
• Initial data for a deformed isolated horizon
• New frontiers in Numerical Relativity