# Binary Black Holes

The first stable simulations in numerical relativity for binary black holes in quasi-circular orbits were performed in 2004. Since that time, many waveforms have been calculated and cataloged. Some waveforms are particularly challenging to compute, especially when the black holes have very large spins, or one black hole is much smaller than the other.

A second challenge is that as a new generation of detectors come online, it is important that numerical relativity simulations also commensurately improve. We are developing new numerical techniques to make these computations more efficient. The new Dendro-GR project to help meet some of these

## Black Holes with Dendro-GR

The Dendro-GR code uses WAMR.

## The Agave code

*A long time ago in a galaxy far, far away...*

The binary black hole problem has fascinated researchers for decades. Some of the first work was done by Larry Smarr and Bryce DeWitt at the Center for Relativity at the University of Texas at Austin.

Later, the Grand Challenge project was organized under the leadership of Richard Matzner, also at the Center for Relativity. The Agave code was developed as part of this collaboration, and development was continued by researchers at UT Austin and Penn State. It's interesting to look back on simulations from the past.

This movie shows the \(g_{xx}\) component of the metric in a grazing collision between two black holes. This simulation uses excision, a technique where part of the computational grid inside the black hole is removed from the domain. The excised regions appear here as circles where \(g_{xx}\) has a constant value. The excision region grows after the black hole merger.

The entire simulation was performed on a single, uniform computational grid that is parallelized with MPI using the Cactus Framework. The computational complexity of the Einstein equations severely limited the grid sizes. This simulation likely used \(81^3\) points, and the outer boundaries of the grid are too close to the black holes. The discretization scale can be seen in the border of the excision region. Simulations were performed on the Cray T3E, such as the one below at the TACC at UT Austin.

Unfortunately, the ADM formalism of the Einstein equations used by Agave was shown to be numerically unstable. This instability is apparent at the end of the simulation, when the magnitude of \(g_{xx}\) begins growing across the gird.