High and Low Dimensions in The Black Hole Negative Mode

The negative mode of the Schwarzschild black hole is central to Euclidean quantum gravity around hot flat space and for the Gregory-Laflamme black string instability. We analyze the eigenvalue as a function of space-time dimension by constructing two perturbative expansions: one for large d and the other for small d-3, and determining as many coefficients as we are able to compute analytically. Joining the two expansions we obtain an interpolating rational function accurate to better than 2% through the whole range of dimensions including d=4.Comment: 17 pages, 4 figures. v2: added reference. v3: published versio

One-Dimensional Approximation of Viscous Flows

Attention has been paid to the similarity and duality between the Gregory-Laflamme instability of black strings and the Rayleigh-Plateau instability of extended fluids. In this paper, we derive a set of simple (1+1)-dimensional equations from the Navier-Stokes equations describing thin flows of (non-relativistic and incompressible) viscous fluids. This formulation, a generalization of the theory of drop formation by Eggers and his collaborators, would make it possible to examine the final fate of Rayleigh-Plateau instability, its dimensional dependence, and possible self-similar behaviors before and after the drop formation, in the context of fluid/gravity correspondence.Comment: 17 pages, 3 figures; v2: refs & comments adde

Non-uniform Black Strings with Schwarzschild-(Anti-)de Sitter Foliation

We present some exact non-uniform black string solutions of 5-dimensional pure Einstein gravity as well as Einstein-Maxwell-dilaton theory at arbitrary dilaton coupling. The solutions share the common property that their 4-dimensional slices are Schwarzchild-(anti-)de Sitter spacetimes. The pure gravity solution is also generalized to spacetimes of dimensions higher than 5 to get non-uniform black branes.Comment: LaTeX 14 pages, 3 eps figures. V2: version appeared in CQ

Rotating nonuniform black string solutions

We explore via linearized perturbation theory the Gregory-Laflamme instability of rotating black strings with equal magnitude angular momenta. Our results indicate that the Gregory-Laflamme instability persists up to extremality for all even dimensions between six and fourteen. We construct rotating nonuniform black strings with two equal magnitude angular momenta in six dimensions. We see a first indication for the occurrence of a topology changing transition, associated with such rotating nonuniform black strings. Charged nonuniform black string configurations in heterotic string theory are also constructed by employing a solution generation technique.Comment: 36 pages, 10 figures, final versio

Instabilities of Black Strings and Branes

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 horizon-topology 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 non-gravitational theories including Yang-Mills theories and Little String Theory.Comment: 119 pages, 16 figures. Invited review for Classical and Quantum Gravit