72 research outputs found
Multiply Unstable Black Hole Critical Solutions
The gravitational collapse of a complex scalar field in the harmonic map is
modeled in spherical symmetry. Previous work has shown that a change of
stability of the attracting critical solution occurs in parameter space from
the discretely self-similarity critical (DSS) solution originally found by
Choptuik to the continuously self-similar (CSS) solution found by Hirschmann
and Eardley. In the region of parameter space in which the DSS is the
attractor, a family of initial data is found which finds the CSS as its
critical solution despite the fact that it has more than one unstable mode. An
explanation of this is proposed in analogy to families that find the DSS in the
region where the CSS is the attractor.Comment: 8 pages, 7 figure
The Nonlinear Sigma Model With Distributed Adaptive Mesh Refinement
An adaptive mesh refinement (AMR) scheme is implemented in a distributed
environment using Message Passing Interface (MPI) to find solutions to the
nonlinear sigma model. Previous work studied behavior similar to black hole
critical phenomena at the threshold for singularity formation in this flat
space model. This work is a follow-up describing extensions to distribute the
grid hierarchy and presenting tests showing the correctness of the model.Comment: 6 pages, 5 figure
Threshold of Singularity Formation in the Semilinear Wave Equation
Solutions of the semilinear wave equation are found numerically in three
spatial dimensions with no assumed symmetry using distributed adaptive mesh
refinement. The threshold of singularity formation is studied for the two cases
in which the exponent of the nonlinear term is either or . Near the
threshold of singularity formation, numerical solutions suggest an approach to
self-similarity for the case and an approach to a scale evolving static
solution for .Comment: 6 pages, 7 figure
Scalar Collapse in AdS
Recently, studies of the gravitational collapse of a scalar field within
spherically symmetric AdS spacetimes was presented in
\cite{Bizon:2011gg,Jalmuzna:2011qw} which showed an instability of pure AdS to
black hole formation. In particular, the work showed that arbitrarily small
initial configurations of scalar field evolved through some number of
reflections off the AdS boundary until a black hole forms. We consider this
same system, extended to include a complex scalar field, and reproduce this
phenomena. We present tests of our numerical code that demonstrate convergence
and consistency. We study the properties of the evolution as the scalar pulse
becomes more compact examining the asymptotic behavior of the scalar field, an
observable in the corresponding boundary CFT. We demonstrate that such BH
formation occurs even when one places a reflecting boundary at finite radius
indicating that the sharpening is a property of gravity in a bounded domain,
not of AdS itself. We examine how the initial energy is transferred to higher
frequencies --which leads to black hole formation-- and uncover interesting
features of this transfer.Comment: 34 pages, 11 figures; Revised to be more consistent with published
version: updated references, an added paragraph, and a subsection remove
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