49 research outputs found
Late-time tails of a Yang-Mills field on Minkowski and Schwarzschild backgrounds
We study the late-time behavior of spherically symmetric solutions of the
Yang-Mills equations on Minkowski and Schwarzschild backgrounds. Using
nonlinear perturbation theory we show in both cases that solutions having
smooth compactly supported initial data posses tails which decay as at
timelike infinity. Moreover, for small initial data on Minkowski background we
derive the third-order formula for the amplitude of the tail and confirm
numerically its accuracy.Comment: 7 pages, 3 figure
On vacuum gravitational collapse in nine dimensions
We consider the vacuum gravitational collapse for cohomogeneity-two solutions
of the nine dimensional Einstein equations. Using combined numerical and
analytical methods we give evidence that within this model the
Schwarzschild-Tangherlini black hole is asymptotically stable. In addition, we
briefly discuss the critical behavior at the threshold of black hole formation.Comment: 4 pages, 4 figure
Equivariant wave maps exterior to a ball
We consider the exterior Cauchy-Dirichlet problem for equivariant wave maps
from 3+1 dimensional Minkowski spacetime into the three-sphere. Using mixed
analytical and numerical methods we show that, for a given topological degree
of the map, all solutions starting from smooth finite energy initial data
converge to the unique static solution (harmonic map). The asymptotics of this
relaxation process is described in detail. We hope that our model will provide
an attractive mathematical setting for gaining insight into
dissipation-by-dispersion phenomena, in particular the soliton resolution
conjecture.Comment: 16 pages, 9 figure
On convergence towards a self-similar solution for a nonlinear wave equation - a case study
We consider the problem of asymptotic stability of a self-similar attractor
for a simple semilinear radial wave equation which arises in the study of the
Yang-Mills equations in 5+1 dimensions. Our analysis consists of two steps. In
the first step we determine the spectrum of linearized perturbations about the
attractor using a method of continued fractions. In the second step we
demonstrate numerically that the resulting eigensystem provides an accurate
description of the dynamics of convergence towards the attractor.Comment: 9 pages, 5 figure
Vacuum gravitational collapse in nine dimensions
We consider the vacuum gravitational collapse for cohomogeneity-two solutions of the nine dimensional Einstein equations. Using combined numerical and analytical methods we give evidence that within this model the Schwarzschild-Tangherlini black hole is asymptotically stable. In addition, we briefly discuss the critical behavior at the threshold of black-hole formation
Tails for the Einstein-Yang-Mills system
We study numerically the late-time behaviour of the coupled Einstein
Yang-Mills system. We restrict ourselves to spherical symmetry and employ
Bondi-like coordinates with radial compactification. Numerical results exhibit
tails with exponents close to -4 at timelike infinity and -2 at future
null infinity \Scri.Comment: 12 pages, 5 figure
Late-time tails of a self-gravitating massless scalar field, revisited
We discuss the nonlinear origin of the power-law tail in the long-time
evolution of a spherically symmetric self-gravitating massless scalar field in
even-dimensional spacetimes. Using third-order perturbation method, we derive
explicit expressions for the tail (the decay rate and the amplitude) for
solutions starting from small initial data and we verify this prediction via
numerical integration of the Einstein-scalar field equations in four and six
dimensions. Our results show that the coincidence of decay rates of linear and
nonlinear tails in four dimensions (which has misguided some tail hunters in
the past) is in a sense accidental and does not hold in higher dimensions.Comment: 10 pages, 6 figures, one reference added, updated to conform with
published versio
Thermal emission from bare quark matter surfaces of hot strange stars
We consider the thermal emission of photons and electron-positron pairs from
the bare quark surface of a hot strange star. The radiation of high-energy (>
20 MeV) equilibrium photons prevails at the surface temperature T_S > 5 x
10^{10} K, while below this temperature, 8 x 10^8 < T_S < 5 x 10^{10} K,
emission of electron-positron pairs created by the Coulomb barrier at the quark
surface dominates. The thermal luminosity of a hot strange star in both photons
and pairs is estimated.Comment: 10 pages, 2 figures, ApJLetters, in pres
Colour-singlet strangelets at finite temperature
Considering massless and quarks, and massive (150 MeV) quarks in
a bag with the bag pressure constant MeV, a colour-singlet
grand canonical partition function is constructed for temperatures
MeV. Then the stability of finite size strangelets is studied minimizing the
free energy as a function of the radius of the bag. The colour-singlet
restriction has several profound effects when compared to colour unprojected
case: (1) Now bulk energy per baryon is increased by about MeV making the
strange quark matter unbound. (2) The shell structures are more pronounced
(deeper). (3) Positions of the shell closure are shifted to lower -values,
the first deepest one occuring at , famous -particle ! (4) The shell
structure at vanishes only at MeV, though for higher
-values it happens so at MeV.Comment: Revtex file(8 pages)+6 figures(ps files) available on request from
first Autho
Two classes of nonlocal Evolution Equations related by a shared Traveling Wave Problem
We consider reaction-diffusion equations and Korteweg-de Vries-Burgers (KdVB)
equations, i.e. scalar conservation laws with diffusive-dispersive
regularization. We review the existence of traveling wave solutions for these
two classes of evolution equations. For classical equations the traveling wave
problem (TWP) for a local KdVB equation can be identified with the TWP for a
reaction-diffusion equation. In this article we study this relationship for
these two classes of evolution equations with nonlocal diffusion/dispersion.
This connection is especially useful, if the TW equation is not studied
directly, but the existence of a TWS is proven using one of the evolution
equations instead. Finally, we present three models from fluid dynamics and
discuss the TWP via its link to associated reaction-diffusion equations