Abstract
We construct solutions of non-uniform black strings in dimensions from D ≈ 9 all the way up to D = ∞, and investigate their thermodynamics and dynamical stability. Our approach employs the large-D perturbative expansion beyond the leading order, including corrections up to 1/D4. Combining both analytical techniques and relatively simple numerical solution of ODEs, we map out the ranges of parameters in which non-uniform black strings exist in each dimension and compute their thermodynamics and quasinormal modes with accuracy. We establish with very good precision the existence of Sorkin’s critical dimension and we prove that not only the thermodynamic stability, but also the dynamic stability of the solutions changes at it.
Highlights
Establishing the existence of an instability of the translationally invariant, uniform black string (UBS) solution is relatively easy, as it only involves the study of linearized mode perturbations: a mode with negative imaginary frequency signals an instability
Ref. [20] obtained the leading order (LO) large-D effective dynamical equations for the system, and performed time evolutions which showed that when D → ∞ the instability ends at inhomogeneous stable black strings
We can further verify the presence of thermodynamically stable nonuniform black strings (NUBS) in D = 11, 12, which are below the critical dimension, as found in [15]
Summary
We begin by briefly recalling the derivation of the effective equations for the dynamics of large-D black strings, and how they reveal the appearance of the non-uniform solutions [20, 29, 31]. The functions m0(t, z) and p0(t, z), which can be regarded as collective variables for the energy and momentum density along the string, must obey R-independent constraints of the form Any solution to these equations gives a (generically time-dependent) black string solution of Einstein’s theory to leading order in 1/n. For it is convenient to choose our length units so that the horizon is at r = 1 in the uniform black string solution — later we will set units differently. Take this solution, m0 = 1, p0 = 0, and perturb it slighty in the form m0 = 1 + δm eΩt+ikz , p0 = δp eΩt+ikz. In our study we will combine analytic and numerical techniques
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