Late-time tails of a Yang–Mills field on Minkowski and Schwarzschild backgrounds

  title={Late-time tails of a Yang–Mills field on Minkowski and Schwarzschild backgrounds},
  author={Piotr Bizo'n and Tadeusz Chmaj and Andrzej Rostworowski},
  journal={Classical and Quantum Gravity},
  pages={F55 - F63}
We study the late-time behaviour 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 possess 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 numerically confirm its accuracy. 

Figures from this paper

A Yang–Mills field on the extremal Reissner–Nordström black hole

We consider a spherically symmetric (magnetic) SU(2) Yang–Mills field propagating on the exterior of the extremal Reissner–Nordström black hole. Taking advantage of the conformal symmetry, we reduce

Hyperboloidal Einstein-matter evolution and tails for scalar and Yang–Mills fields

We show how matter can be included in a constrained ADM-like formulation of the Einstein equations on constant mean curvature surfaces. Previous results on the regularity of the equations at future

Global dynamics of a Yang-Mills field on an asymptotically hyperbolic space

We consider a spherically symmetric (purely magnetic) SU(2) Yang-Mills field propagating on an ultrastatic spacetime with two asymptotically hyperbolic regions connected by a throat of radius

Asymptotics of Schwarzschild black hole perturbations

We study linear gravitational perturbations of Schwarzschild spacetime by solving numerically Regge–Wheeler–Zerilli equations in a time domain using hyperboloidal surfaces and a compactifying radial

Gravitational perturbations of Schwarzschild spacetime at null infinity and the hyperboloidal initial value problem

We study gravitational perturbations of Schwarzschild spacetime by solving a hyperboloidal initial value problem for the Bardeen–Press equation. Compactification along hyperboloidal surfaces in a

A scattering theory construction of dynamical vacuum black holes

We construct a large class of dynamical vacuum black hole spacetimes whose exterior geometry asymptotically settles down to a fixed Schwarzschild or Kerr metric. The construction proceeds by solving

Critical phenomena in the general spherically symmetric Einstein-Yang-Mills system

We study critical behavior in gravitational collapse of a general spherically symmetric Yang-Mills field coupled to the Einstein equations. Unlike the magnetic ansatz used in previous numerical work,

Testing the black hole ‘no-hair’ hypothesis

Black holes (BHs) in general relativity (GR) are very simple objects. This property, that goes under the name of ‘no-hair’, has been refined in the last few decades and admits several versions. The

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.



Late-time Evolution of the Yang-Mills Field in the Spherically Symmetric Gravitational Collapse

We investigate the late-time evolution of theYang-Mills field in the self-gravitating backgrounds:Schwarzschild and Reissner-Nordstrom spacetimes. Thelate-time power-law tails develop in the

The global existence of Yang-Mills-Higgs fields in 4-dimensional Minkowski space

In this paper and its sequel we shall prove the local and then the global existence of solutions of the classical Yang-Mills-Higgs equations in the temporal gauge. This paper proves local existence

Asymptotic properties of the solutions of linear and nonlinear spin field equations in Minkowski space

In this paper I will first derive, based on energy estimations and geometric invariance, the asymptotic behavior of solutions of linear spin field equations in Minkowski space. It generalizes the

Spectral decomposition of the perturbation response of the Schwarzschild geometry.

  • Leaver
  • Physics, Mathematics
    Physical review. D, Particles and fields
  • 1986
The branch-cut integral produces a weak late-time radiative power-law decay tail that will characterize the astrophysically observed radiation spectrum for times subsequent to the exponential decay of the quasinormal ringing.

Finite energy solutions of the Yang-Mills equations in $\mathbb{R}^{3+1}$

Yang-Mills equations in R3+1 is well-posed in the energy norm. This means that for an appropriate gauge condition, we construct local, unique solutions in a time interval which depends only on the

Global existence of solutions of the Yang–Mills equations on globally hyperbolic four dimensional Lorentzian manifolds

We prove global solvability of the Cauchy problem for the Yang-Mills equations on smooth globally hyperbolic four dimensional Lorentzian manifolds.

Space-time symmetries in gauge theories

A general definition of symmetries of gauge fields is proposed and a method developed for constructing symmetric fields for an arbitrary gauge group. Scalar fields occur naturally in the formalism

The scattering of certain Yang-Mills fields

The Yang-Mills fields considered by us in an earlier paper are asymptotically non-interacting. Also any free field is an incoming field for some Yang-Mills field.

Asian J

  • Math. 1, 530
  • 1997