

Research
Einstein's equations are a set of coupled, nonlinear partial differential
equations, and as a result of their complexity, solutions may oftentimes
only be found by numerical techniques. The problem of finding these solutions
for astrophysically relevant situations is the essence of Numerical Relativity.
We detail here a few of the facets of this ongoing effort, and highlight some
of the active research being done by this group.



Singularity Handling
The physical singularities inherent to black hole solutions pose
a critical problem to those who wish to use standard finite differencing
techiques and they must handled by coordinate choices, puncture techniques,
or singularity excision.




Formulation of the Einstein Equations
The very form in which the equations are written has a drastic impact
upon the stability of any evolution, and this is doubly true here. Over the
past few years interest has risen steadily in careful analysis of the formulation
of the Einstein equations.


Binary BlackHole Initial Data
Any evolution scheme begins with a specification of initial
data. Our use of excision techniques for singularity handling
allows us to use natural superposed KerrSchildtype data,
conditioned by a constraint solver, as our starting point. We
have produced different variants on this superposition scheme,
with desirable near and farfield limits.




Binary BlackHole Collisions
Beginning with superposed initial data, we are testing the
limits of newer evolution schemes (e.g., BSSN) to evolve a
strongfield binary collision in full 3D, through the formation
of a common apparent horizon, and towards the "ringdown" regime.


Apples With Apples
Penn State is a participant of the "Apples with Apples" project, for
comparing different numerical codes, and devising useful tests for
successful NR codes. A results page is maintained here.
