Eric Hirschmann's Research
- Several months ago, we considered the stability of a family of solutions in
Brans-Dicke theory. They had been suggested as possible "approximate"
black holes in numerical relativity. We examined both linear and non-linear
perturbations of the solutions. The results are presented most completely in
paper that appeared in Phys Rev D. I also gave a presentation on
this work at the
Marcel Grossmann meeting in Jerusalem. The contribution to
the proceedings is here.
- We are working on a project to solve the axisymmetric Einstein-scalar
equations. Our approach is to use the (2+1)+1
reduction of the Einstein equations. My current
of the equations
is quite preliminary, but a start. As a
to this problem, we
are considering flat space scalar electrodynamics in axisymmetry. And as a warmup
to scalar E&M, we have looked at the scalar wave equation in axisymmetry.
Matt did some initial work
on this in the context of using RNPL. Our scheme uses the first order form
for the equations and uses leapfrog differencing. We have modified the
regularity conditions so we do not get the instability Matt saw in the
above. However, at late times the axis does become unstable.
Two MPEG movies are available. They show two parts of the evolution of a
time symmetric pulse on a grid 129 by 257. The first
runs from t = 0 to about t = 600 and the
runs from t = 600 to about t = 1200.
- With Matt and Robert Marsa, I have also begun an investigation of
the EYMH equations in a general spherically symmetric gauge and with
a general spherically symmetric connection. The working
for that also
needs some work, but is a bit further along. Much of the work in this
area has been to consider the static equations in spherical symmetry.
However, there are suggestions that many of these solutions may serve
as critical solutions to black hole formation. I gave a talk describing
some of the background and possible directions this work could take.
The outline for the talk is here.
- I have also worked with Steve Liebling on texture collapse. I have
included some of our
early results of collapse of a Hopf texture with
toroidally symmetric initial data. Steve has a nice page of some
3D evolutions. More complete results are in our
together with some
of 2D evolutions.
Updated another time January 12, 1998.
Eric W. Hirschmann