Nonuniform black strings in various dimensions

Abstract

The nonuniform black strings branch, which emerges from the critical GregoryLaflamme string, is numerically constructed in dimensions 6 ≤ D ≤ 11 and extended into the strongly non-linear regime. All the solutions are more massive and less entropic than the marginal string. We find the asymptotic values of the mass, the entropy and other physical variables in the limit of large horizon deformations. By explicit metric comparison we verify that the local geometry around the "waist" of our most nonuniform solutions is cone-like with less than 10% deviation. We find evidence that in this regime the characteristic length scale has a power-law dependence on a parameter along the branch of the solutions, and estimate the critical exponent.

Critical behavior of the black hole/black string transition

“…Surprisingly, there seems to be a relation between this system in D − 1 dimensions and the black hole/black string system in D dimensions [24]. 8 In order to show such a critical behavior in the black hole/black string transition, we fit the data of different physical quantities close to the transition with an appropriate ansatz, that is . We show different localized black hole and non-uniform black string horizons that approach the cone shape from above/below and from right/left, respectively.…”

STABILITY OF AdS BLACK STRINGS

“…This metric form generalizes for the AdS case the usual Λ = 0 NUBS ansatz used e.g. in [3], [5], [6], which is recovered for κ = 1 and b = 1/f = 1 − (r 0 /r) d−4 , a = 1. Following the standard approach, we perform an expansion around the UBS of the form…”

“…Following this discovery, a branch of nonuniform black string (NUBS) solutions was found perturbatively from the critical GL string [2], [3], [4]. This nonuniform branch was subsequently numerically extended into the full nonlinear regime in [3], [5], [6] (see [7], [8] for reviews of this topic).…”

Black Holes in Higher-Dimensional Gravity

“…Since in many cases the Einstein equations become too complicated to be amenable to analytical methods, even after using symmetries and ansätze, the only way to proceed in the non-linear regime is to try to solve them numerically. Especially for KK black holes these techniques have been successfully applied for non-uniform black strings [37,38,39,40,41,42] and localized black holes [46,47,48] (see Sec. 3).…”

“…An interesting property that has been found in this context is the existence of a critical dimension [39] where the transition of the uniform black string into the non-uniform black string changes from first order into second order. Moreover, it has been shown [55,56,57,41] that the localized black hole phase meets the non-uniform black string phase in a horizon-topology changing merger point. Turning to more recent developments, we note that the new multi-black hole configurations of Ref.…”