Project: Event Horizons in Numerical Relativity
Project: Event Horizons in Numerical Relativity The NCSA/WashU Event Horizon project involves locating and analyzing event horizons in dynamical axisymmetric spacetimes. The method of location is based on casting the problem of finding the EH location as a single PDE (rather than a set of ODE's common in photon-tracking EH finders) and then integrating this PDE backwards in time, which is the physically stable integration direction. The analysis tools we have developed include: Geometrical measures of the horizon such as area, ratio of equatorial to polar circumference and gaussian curvature; Location of the null generators of the EH; and application of membrane paradigm-like properties to the truly dynamical EH.
Along the way, we have create many images and movies of the work. Our EH gallery contains extensive images and movies showing details of many of the interesting phenomena we have seen, and we feel it is extremely effective in demonstrating the physics and dynamics of Black Hole Event Horizons.
Much work has been completed on the geometry of horizons in several spacetimes. We have spent large amounts of time analyzing the caustic structure of the 2 black hole collision and how it affects our method. Also we have been comparing geometric properties against global theorems and expected results from perturbation theory (eg, Quasi-normal mode ringing of the horizon).Currently, a second paper on the analytic tools we have developed is in preparation. This paper will report on the succesful implementation of the geometric measures, generator location routines, and membrane paradigm like quantities in our EH location code. It will also present an overview of the formalism needed to find these quantities and some testbed cases in which these quantities are examined and tested. This paper will be available by Jan 1, 1996.
As a long term goal, we would like to use these tools to examine the dynamics, physics, and geometry of several interesting black hole spacetimes, including excepetionally highly distorted spacetimes and colliding black holes. One of the most interesting problems is the maximum distortion which an Event Horizon can undergo. Studies by Bernstien and Brandt show Apparent Horizons with huge non-sphericities. If we could find such Event Horizons, it may tell us about possible formulations of a vacuum hoop conjecture.
Several publications have been completed on this work, and several more are in progress. Related papers on our server are:
- Dynamics of Apparent and Event Horizons
- Phys. Rev. Lett. 74 (1995) 630-633.
- Event Horizons in Numerical Relativity I: Methods and Tests ,
- Submitted to Phys. Rev. D. Also gr-qc/9412068
- Event Horizons of Numerical Black Holes,
- MG7 Proceedings. Also gr-qc/9412056
Also, this work was the basis for a publication by Matzner et al on the geometry of the horizon of the collision of two black holes. That paper is also available on our server.
- Geometry of a Black Hole Collision
- Richard A. Matzner, H. E. Seidel, S. Shapiro, L. Smarr, W-M Suen, Saul Teukolsky, J. Winicour
The spacetimes in which we find the EH come from the efforts in distorted and colliding axisymmetric black holes and rotating black holes. The geometry of the horizon is inseparably tied to the geometries of the spacetime, so the analysis of the EH would be impossible without the analysis and succesful evolution of these 2D axisymmetric spacetimes.