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 $t^{-4}$ 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

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 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

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 $i^+$ 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 $u$ and $d$ quarks, and massive (150 MeV) $s$ quarks in a bag with the bag pressure constant $B^{1/4} = 145$ MeV, a colour-singlet grand canonical partition function is constructed for temperatures $T = 1-30$ 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 $250$ 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 $A$-values, the first deepest one occuring at $A=2$, famous $H$-particle ! (4) The shell structure at $A=2$ vanishes only at $T\sim 30$ MeV, though for higher $A$-values it happens so at $T\sim 20$ 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