Instabilities of black strings and branes

Abstract

We review recent progress on the instabilities of black strings and branes both for pure Einstein gravity as well as supergravity theories which are relevant for string theory. We focus mainly on Gregory-Laflamme instabilities. In the first part of the review we provide a detailed discussion of the classical gravitational instability of the neutral uniform black string in higher dimensional gravity. The uniform black string is part of a larger phase diagram of Kaluza-Klein black holes which will be discussed thoroughly. This phase diagram exhibits many interesting features including new phases, non-uniqueness and horizontopology changing transitions. In the second part, we turn to charged black branes in supergravity and show how the Gregory-Laflamme instability of the neutral black string implies via a boost/U-duality map similar instabilities for non-and near-extremal smeared branes in string theory. We also comment on instabilities of D-brane bound states. The connection between classical and thermodynamic stability, known as the correlated stability conjecture, is also reviewed and illustrated with examples. Finally, we examine the holographic implications of the Gregory-Laflamme instability for a number of nongravitational theories including Yang-Mills theories and Little String Theory.

Probing the hydrodynamic limit of (super)gravity

“…[15]). Understanding these properties is interesting from a pure general relativistic point of view viz.…”

“…The expressions for these functions are however very long and have therefore been omitted. After some work, one finds that the equation is solved by 15) JHEP04 (2015)171 where the terms containing the two integration constants c (1) Tr and c (2) Tr correspond to the homogeneous solution. The entire family of homogeneous solutions to equation (A.14) of course has an additional one-parameter freedom which has been absorbed in the particular solution Trf (s) ij (r) and been used to ensure horizon regularity.…”

Thermodynamic and classical instability of AdS black holes in fourth-order gravity

“…In this case, its linearized equation reduces tō 13) which is exactly the linearized equation around the SAdS black hole in Einstein gravity. From the observation 3 of figure 4, the GL instability disappears at M d = 0, which may imply that the SAdS black hole is stable against the s-mode metric perturbation.…”

Black Holes in Higher-Dimensional Gravity

“…The values of k c for d = 4, ..., 14, as obtained in [53,37,39], are listed e.g. in Table 1 of [3]. The critical wave-number k c marks the lower bound of the possible wavelengths for which there is an unstable mode and is called the threshold mode.…”

“…Here γ is a number representing the slope of the curve that describes the non-uniform string branch near µ = µ GL (see Table 3 in [3] for the values of γ for 4 ≤ d ≤ 14 obtained from the data of [53,54,37,38,39]). The qualitative behavior of the non-uniform string branch depends on the sign of γ.…”