Abstract
We construct static vacuum localized black holes and non-uniform black strings in ten spacetime dimensions, where one of the dimension is compactified on a circle. We study the phase diagram of black objects with these boundary conditions, especially near the critical point where localized black holes and non-uniform black strings merge. Remarkably, we find that the merger happens at a cusp in the phase diagram. We verify that the critical geometry is controlled by a Ricci-flat double-cone as previously predicted. However, unlike the lower dimensional cases, we find that physical quantities approach to their critical values according to a power law plus a logarithmic correction. We extract the critical exponents and find very good agreement with the predictions from the double-cone geometry. According to holography, localized black holes and black strings are dual to thermal states of (1 + 1)-dimensional SU(N) maximal Super-Yang Mills theory compactified on a circle; we recover and extend the details of the (recently found) 1st order phase transition in this system from the gravity side.
Highlights
IntroductionBased on entropic arguments, [7] conjectured that unstable uniform black string (UBS) would evolve into an array of localized black holes through a dynamical topology change transition; the latter can only happen through a singularity and the evolution of the Gregory and Laflamme (GL) instability of black strings could potentially constitute a counter-example of the weak cosmic censorship conjecture [18, 19] around such spacetimes
One of the most extensively studied models in this setting is that of Md = Minkd and N1 = S1, a circle of length L
We first consider the behavior of the various thermodynamic quantities along each branch of solutions and the phase diagrams, and we focus on the horizon geometry
Summary
Based on entropic arguments, [7] conjectured that unstable UBS would evolve into an array of localized black holes through a dynamical topology change transition; the latter can only happen through a singularity and the evolution of the GL instability of black strings could potentially constitute a counter-example of the weak cosmic censorship conjecture [18, 19] around such spacetimes This scenario was recently confirmed by [20, 21], using numerical relativity techniques.. Motivated by geometrical considerations, [34] conjectured that the NUBS and LOC branches should merge at a topology changing critical solution governed by a Ricci-flat double-cone This conjecture was tested from the black string side in [35], and later in various dimensions in [13]. That the methods of [16] did not allow them to study critical solutions in detail and our results complement theirs
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