- 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 a 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 writeup of the equations is quite preliminary, but a start. As a warmup 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 (947k) runs from t = 0 to about t = 600 and the second (2166k) 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 notes 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 paper together with some movies of 2D evolutions.

Eric W. Hirschmann ehirsch@dirac.ph.utexas.edu