Caged Black Holes: Black Holes in Compactified Spacetimes II - 5d Numerical Implementation

Abstract

We describe the first convergent numerical method to determine static black hole solutions (with S^3 horizon) in 5d compactified spacetime. We obtain a family of solutions parametrized by the ratio of the black hole size and the size of the compact extra dimension. The solutions satisfy the demanding integrated first law. For small black holes our solutions approach the 5d Schwarzschild solution and agree very well with new theoretical predictions for the small corrections to thermodynamics and geometry. The existence of such black holes is thus established. We report on thermodynamical (temperature, entropy, mass and tension along the compact dimension) and geometrical measurements. Most interestingly, for large masses (close to the Gregory-Laflamme critical mass) the scheme destabilizes. We interpret this as evidence for an approach to a physical tachyonic instability. Using extrapolation we speculate that the system undergoes a first order phase transition.

arXiv comment42 pages, 19 eps figures; v2: 3 references added, version to appear in Phys.Rev.D

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Cited by in corpus (52)

• Spectral Methods for Numerical Relativity
• A new approach to static numerical relativity, and its application to Kaluza-Klein black holes
• The Phase Transition between Caged Black Holes and Black Strings - A Review
• Instabilities of Black Strings and Branes
• A critical dimension in the black-string phase transition
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• Connecting black holes and black strings
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• General Definition of Gravitational Tension
• Black Rings, Boosted Strings and Gregory-Laflamme
• On Black-Brane Instability In an Arbitrary Dimension
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• New nonuniform black string solutions
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• New Phases of Near-Extremal Branes on a Circle
• Stable non-uniform black strings below the critical dimension
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• Origin of black string instability
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• Harrison transformation and charged black objects in Kaluza-Klein theory
• LG (Landau-Ginzburg) in GL (Gregory-Laflamme)
• Higher dimensional black holes
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• Phases of Holographic Hawking Radiation on spatially compact spacetimes
• Critical Kaluza-Klein black holes and black strings in D = 10
• Gregory-Laflamme and Superradiance encounter Black Resonator Strings
• Three-Charge Black Holes on a Circle
• Phases of Higher Dimensional Black Holes
• The decay of hot KK space
• Charged black holes in compactified spacetimes
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• Black Topologies Production in Extra Dimensions
• First Law and a Variational Principle for Static Asymptotically Randall-Sundrum Black Holes
• The Low Energy Limit of BFSS Quantum Mechanics