415 research outputs found
Final State of Gregory-Laflamme Instability
We describe the behavior of a perturbed 5-dimensional black string subject to
the Gregory-Laflamme instability. We show that the horizon evolves in a
self-similar manner, where at any moment in the late-time development of the
instability the horizon can be described as a sequence of 3-dimensional
spherical black holes of varying size, joined by black string segments of
similar radius. As with the initial black string, each local string segment is
itself unstable, and this fuels the self-similar cascade to (classically)
arbitrarily small scales; in the process the horizon develops a fractal
structure. In finite asymptotic time, the remaining string segments shrink to
zero-size, yielding a naked singularity. Since no fine-tuning is required to
excite the instability, this constitutes a generic violation of cosmic
censorship. We further discuss how this behavior is related to satellite
formation in low-viscosity fluid streams subject to the Rayleigh-Plateau
instability, and estimate the fractal dimension of the horizon prior to
formation of the naked singularity.Comment: 27 pages, 6 Figures. Chapter of the book `Black Holes in Higher
Dimensions' to be published by Cambridge University Press (editor: G.
Horowitz
Scalar field confinement as a model for accreting systems
We investigate the possibility to localize scalar field configurations as a
model for black hole accretion. We analyze and resolve difficulties encountered
when localizing scalar fields in General Relativity. We illustrate this ability
with a simple spherically symmetric model which can be used to study features
of accreting shells around a black hole. This is accomplished by prescribing a
scalar field with a coordinate dependent potential. Numerical solutions to the
Einstein-Klein-Gordon equations are shown, where a scalar filed is indeed
confined within a region surrounding a black hole. The resulting spacetime can
be described in terms of simple harmonic time dependence.Comment: 18 pages; accepted for publication in Classical and Quantum Gravit
Unstable horizons and singularity development in holography
In holographic applications one can encounter scenarios where a
long-wavelength instability can arise. In such situations, it is often the case
that the dynamical end point of the instability is a new equilibrium phase with
a nonlinear scalar hair condensate outside the black hole horizon. We here
review holographic setups where symmetric horizons suffer from long-wavelength
instabilities where a suitable equilibrium condensate phase does not exist. We
study the dynamics of the simplest model in this exotic class, and show that it
uncovers arbitrarily large curvatures in the vicinity of the horizon which
asymptotically turn such region singular, at finite time with respect to the
boundary theory.Comment: 38 pages, 41 figure
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