Abstract
We explore via linearized perturbation theory the Gregory–Laflamme instability of the black string solutions of Einstein's equations with negative cosmological constant recently discussed in literature. Our results indicate that the black strings whose conformal infinity is the product of time and Sd−3×S1 are stable for large enough values of the event horizon radius. All topological black strings are also classically stable. We argue that this provides an explicit realization of the Gubser–Mitra conjecture.
Highlights
In 1993, Gregory and Laflamme (GL) made the surprising discovery that the extended black objects appearing in higher dimensions are classically unstable [1]
The simplest extended black object in general relativity is found by trivially extending to d-spacetime dimensions the Schwarzschild black hole solution in d − 1 dimensions and corresponds to a uniform black string (UBS) with horizon topology Sd−3 × S1
The anti-de Sitter (AdS) natural counterparts of the Schwarzschild black string have been considered for the first time in [9], for the d = 5 case
Summary
In 1993, Gregory and Laflamme (GL) made the surprising discovery that the extended black objects appearing in higher dimensions are classically unstable [1]. One expects a richer structure in this case, since the cosmological constant introduces another scale in the theory This type of solutions provides a new laboratory to test the Gubser-Mitra (GM) conjecture [16], that correlates the dynamical and thermodynamical stability for systems with translational symmetry and infinite extent. In this conjecture, the appearance of a negative specific heat is related to the onset of a classical instability. The final Section contains a discussion of the GM conjecture for AdS black strings together with our conclusions
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