Stabilizing homogeneous black strings in AdS
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Springer
Received: September 13, Revised: November 22, Accepted: December 23, Published: January 9,
2019 2019 2019 2020
Adolfo Cisterna,a Carla Henr´ıquez-B´ aezb and Julio Olivab a
Vicerrector´ıa Acad´emica, Universidad Central de Chile, Toesca 1783, Santiago, Chile b Departamento de F´ısica, Universidad de Concepci´ on, Casilla 160-C, Concepci´ on, Chile
E-mail: [email protected], [email protected], [email protected] Abstract: It is known that homogenous black strings in flat spacetime are unstable under long wavelength perturbations. Recently, by including scalar fields that depend on the extended coordinates only, homogenous black strings have been constructed in the presence of a negative cosmological constant, therefore implying that generic perturbations will contain both metric and scalar fluctuations. Here we show that for such generic perturbations homogeneous black strings with a negative cosmological constant are perturbatively stable at linear level, regardless the size of the Schwarzschild-AdS black hole located on the brane. Keywords: Black Holes, Classical Theories of Gravity, p-branes ArXiv ePrint: 1909.05404
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP01(2020)052
JHEP01(2020)052
Stabilizing homogeneous black strings in AdS
Contents 1
2 Homogeneous black strings in AdS
2
3 Linear perturbations
2
4 Further remark
4
1
Introduction
In General Relativity (GR) in vacuum, one can trivially oxidate black holes to create homogeneous black strings and black p-branes in higher dimensions. These objects are an explicit example of the new phenomena that higher-dimensional gravity offers [1]. Indeed, they exhibit a very rich dynamics since they were proved to suffer from the so-called Gregory-Laflamme (GL) instability [2], a long-wavelength perturbative instability triggered by a mode that travels along the extended direction of the horizon, mimicking the spectrum of the Rayleigh-Plateau instability in fluid dynamics [3]. Beyond the validity of the linear regime, there is enough evidence that for long times, the non-linear effects of GR trigger a violation of cosmic censorship, since the black string horizon will pinch-off in a finite amount of time as seen by an asymptotic observer [4, 5]. Such instability pervades asymptotically flat, black objects in higher dimensions, leading to a similar pinch-off of the rapidly rotating Black Ring horizon [6], as well as of the rapidly rotating Myers-Perry black hole in dimensions D ≥ 6 [7]. It is known that the inclusion of a negative cosmological constant spoils any direct, homogeneous oxidation of the asymptotically AdS black holes (see e.g. [8]), nevertheless, as recently reported in [9] this obstruction can be circumvented in five dimensions by the presence of a massless scalar ψ (y) such that dψ (y) = λdy, where the integration constant λ turns out to be fixed in terms of the bared cosmological constant, and y stands for the coordinate along the extended direction.1 This construction can be exten
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