We study gravitational collapse of an SU(2) Yang-Mills field
in spherical symmetry. We begin by reproducing the
static Einstein-Yang-Mills solution published by Bartnik and
McKinnon in 1988, found by a shooting technique.
Next, we conduct a dynamical evolution of kink-type
initial data. It is found that the solution "slides onto" the
Bartnik-McKinnon solution, stays there for a while, then either
disperses to infinity or forms a black hole. By sufficient binary-search
fine-tuning, we can find the (unstable) critical solution balancing
between these two types of behavior.
There are two types of behavior for this critical solution,
Type I and Type II. Type
I is studied with an
RNPL code, while Type II needs adaptive mesh refinement for a
meaningful investigation, so we modified an existing adaptive code to
investigate Type II behavior rather briefly.
We verify some of the results of Choptuik, Chmaj and Bizon
(1996). Among these are the universal time scaling law for Type I behavior (our
critical exponents are -0.567 for a kink-type initial data and -0.569 for a tanh
initial data form). The time scaling law
describes for how long (in proper time of an
observer at r=0) the solutions sticks to the static one
before it "peels off". We also verify some Type II scale echoing
with the
adaptive code, and find a scale periodicity exponent of 0.75,
which also agrees with the 0.74 of Choptuik et al.
- Document PDF
- Mpegs
- W vs. r (347K) -- Yang-Mills potential slides onto Bartnik-McKinnon
solution
- 2m /r vs. r (340K) -- Type I (sub-)critical solution
- 2m / r vs. ln r
(1311K: Warning! Big!) -- Scale echoing, color-coded grid size
- References
- Bartnik and McKinnon, Phys. Rev. Lett.
61, 141-144 (1988)
-
Choptuik, Chmaj and Bizon,
gr-qc/9603051 and
Phys. Rev. Lett. 77, 424-427 (1996)