36 research outputs found
Nonlinear perturbations of the Kaluza-Klein monopole
We consider the nonlinear stability of the Kaluza-Klein monopole viewed as
the static solution of the five dimensional vacuum Einstein equations. Using
both numerical and analytical methods we give evidence that the Kaluza-Klein
monopole is asymptotically stable within the cohomogeneity-two biaxial Bianchi
IX ansatz recently introduced in \cite{bcs}. We also show that for sufficiently
large perturbations the Kaluza-Klein monopole loses stability and collapses to
a Kaluza-Klein black hole. The relevance of our results for the stability of
BPS states in M/String theory is briefly discussed.Comment: 4 pages, 4 figure
Anomalously small wave tails in higher dimensions
We consider the late-time tails of spherical waves propagating on
even-dimensional Minkowski spacetime under the influence of a long range radial
potential. We show that in six and higher even dimensions there exist
exceptional potentials for which the tail has an anomalously small amplitude
and fast decay. Along the way we clarify and amend some confounding arguments
and statements in the literature of the subject.Comment: 13 page
Scalar field critical collapse in 2+1 dimensions
We carry out numerical experiments in the critical collapse of a spherically
symmetric massless scalar field in 2+1 spacetime dimensions in the presence of
a negative cosmological constant and compare them against a new theoretical
model. We approximate the true critical solution as the Garfinkle
solution, matched at the lightcone to a Vaidya-like solution, and corrected to
leading order for the effect of . This approximation is only
at the lightcone and has three growing modes. We {\em conjecture} that
pointwise it is a good approximation to a yet unknown true critical solution
that is analytic with only one growing mode (itself approximated by the top
mode of our amended Garfinkle solution). With this conjecture, we predict a
Ricci-scaling exponent of and a mass-scaling exponent of
, compatible with our numerical experiments.Comment: 27 page
Critical behavior in vacuum gravitational collapse in 4+1 dimensions
We show that the 4+1 dimensional vacuum Einstein equations admit
gravitational waves with radial symmetry. The dynamical degrees of freedom
correspond to deformations of the three-sphere orthogonal to the plane.
Gravitational collapse of such waves is studied numerically and shown to
exhibit discretely self-similar Type II critical behavior at the threshold of
black hole formation.Comment: 4 pages, 7 figure
Fractal Threshold Behavior in Vacuum Gravitational Collapse
We present the numerical evidence for fractal threshold behavior in the five
dimensional vacuum Einstein equations satisfying the cohomogeneity-two triaxial
Bianchi type-IX ansatz. In other words, we show that a flip of the wings of a
butterfly may influence the process of the black hole formation.Comment: 4 pages, 6 figures, minor change
Codimension-two critical behavior in vacuum gravitational collapse
We consider the critical behavior at the threshold of black hole formation
for the five dimensional vacuum Einstein equations satisfying the
cohomogeneity-two triaxial Bianchi IX ansatz. Exploiting a discrete symmetry
present in this model we predict the existence of a codimension-two attractor.
This prediction is confirmed numerically and the codimension-two attractor is
identified as a discretely self-similar solution with two unstable modes.Comment: 4 pages, 5 figures, typos correcte
A note on late-time tails of spherical nonlinear waves
We consider the long-time behavior of small amplitude solutions of the
semilinear wave equation in odd spatial
dimensions. We show that for the quadratic nonlinearity () the tail has an
anomalously small amplitude and fast decay. The extension of the results to
more general nonlinearities involving first derivatives is also discussed.Comment: 7 page