Highly deformed non-uniform black strings in six dimensions

We study phases of equilibrium Hawking radiation in d-dimensional holographic CFTs on spatially compact spacetimes with two black holes. In the particular phases chosen the dual (d + 1)-dimensional bulk solutions describe a variety of black funnels and droplets. In the former the CFT readily conducts heat between the two black holes, but it in the latter such conduction is highly suppressed. While the generic case can be understood in certain extreme limits of parameters on general grounds, we focus on CFTs on specific geometries conformally equivalent to a pair of d ≥ 4 AdS d -Schwarzschild black holes of radius R. Such cases allow perturbative analyses of non-uniform funnels associated with Gregory-Laflamme zero-modes. For d = 4 we construct a phase diagram for pure funnels and droplets by constructing the desired bulk solutions numerically. The fat non-uniform funnel is a particular interesting phase that dominates at small R (due to having lowest free energy) despite being sub-dominant in the perturbative regime. The uniform funnel dominates at large R, and droplets and thin funnels dominate at certain intermediate values. The thin funnel phase provides a mystery as it dominates over our other phases all that way to a critical R turn beyond which it fails to exist. The free energy of the system thus appears to be discontinuous at R turn , but such discontinuities are forbidden by the 2nd law. A new more-dominant phase is thus required near R turn but the nature of this phase remains unclear.

Section: Diagnosticssupporting

confidence: 69%

Phases of holographic Hawking radiation on spatially compact spacetimes

Marolf

Santos

2019

“…11 We are able to resolve four turning points. Moreover, we fit the physical observables of localized black holes close to the transit solution to scaling ansätze with only discrete scaling symmetry.…”

Section: Jhep08(2017)049mentioning

confidence: 99%

Critical behavior of the black hole/black string transition

Kalisch

Moeckel

Ammon

2017

We numerically construct static localized black holes in five and six spacetime dimensions which are solutions to Einstein's vacuum field equations with one compact periodic dimension. In particular, we investigate the critical regime in which the poles of the localized black hole are about to merge. A well adapted multi-domain pseudo-spectral scheme provides us with accurate results and enables us to investigate the phase diagram of those localized solutions within the critical regime, which goes far beyond previous results. We find that in this regime the phase diagram possesses a spiral structure adapting to the one recently found for non-uniform black strings. When approaching the common endpoint of both phases, the behavior of physical quantities is described by complex critical exponents giving rise to a discrete scaling symmetry. The numerically obtained values of the critical exponents agree remarkably well with those derived from the double-cone metric.

“…The results up to order 1/n for the stress tensor of static solutions and for all other quantities in this section can be found in appendix B. For time-independent solutions we find convenient to define the mass density along the string (adequately rescaled to absorb n-dependent prefactors 10 ), 16) and the tension…”

Section: Physical Magnitudesmentioning

confidence: 99%

Phases and stability of non-uniform black strings

Luna

Montero

Suzuki

et al. 2018

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/D 4 . 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.