A critical dimension in the black-string phase transition

Abstract

In spacetimes with compact dimensions there exist several black object solutions including the black-hole and the black-string. These solutions may become unstable depending on their relative size and the relevant length scale set by the compact dimensions. The transition between these solutions raises puzzles and addresses fundamental questions such as topology change, uniquenesses and cosmic censorship. Here, we consider black strings wrapped over the compact circle of a $d$-dimensional cylindrical spacetime. We construct static perturbative non-uniform string solutions around the instability point of a uniform string. First we compute the instability mass for a large range of dimensions, $d$, and find that it follows essentially an exponential law ${\gamma }^d$, where $\gamma$ is a constant. Then we determine that there is a critical dimension, $d_{\ast }=13$, such that for $d\le d_{\ast }$ the phase transition between the uniform and the non-uniform strings is of first order, while for $d>d_{\ast }$, it is, surprisingly, of higher order.

1+8 pages, 2 eps figures; v2: improved discussions; a minor error in evaluating ${\mu }^{(1)}$ is corrected; references added

References in corpus (26)

• Black Strings and p-Branes are Unstable
• The Instability of Charged Black Strings and p-Branes
• Static Axisymmetric Vacuum Solutions and Non-Uniform Black Strings
• On non-uniform black branes
• Fate of the Black String Instability
• Classical and Thermodynamic Stability of Black Branes
• Instability of charged black holes in anti-de Sitter space
• Topology change in General Relativity and the black-hole black-string transition
• Towards the Final Fate of an Unstable Black String
• Black Holes on Cylinders
• Properties of Kaluza-Klein black holes
• Unstable Horizons
• Small Black Holes on Cylinders
• New Phase Diagram for Black Holes and Strings on Cylinders
• From Black Strings to Black Holes
• Phase Structure of Black Holes and Strings on Cylinders
• Caged Black Holes: Black Holes in Compactified Spacetimes I -- Theory
• Black holes on cylinders are not algebraically special
• Caged Black Holes: Black Holes in Compactified Spacetimes II - 5d Numerical Implementation
• Black Hole Evaporation and Large Extra Dimensions
• Evidence that highly non-uniform black strings have a conical waist
• Stability and the negative mode for Schwarzschild in a finite cavity
• Inhomogeneous Near-extremal Black Branes
• Playing with Black Strings
• Speculative generalization of black hole uniqueness to higher dimensions
• Initial Data for Black Holes and Black Strings in 5d

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