Isometric Embeddings in Binary Black Hole Merger Simulations

The isometric embedding of black hole apparent horizons in flat geometry is useful both for visualizing the horizon structure and for computing quasilocal quantities such as mass, energy, and angular momentum. We have previously presented two new approaches to this problem and confirmed that the results converge and agree with the expected. Recently, we have implemented both solvers in SpEC and used them to compute the embeddings in multiple binary black hole merger simulations with different spin and mass configurations. These embeddings show that the intrinsic shape of horizons can many times differ from the coordinate shape based on the gauge conditions. Additionally, comparing the results of the radically different methods gives us a clue of when an isometric embedding exists for the numerical horizons. In this presentation, we will quickly review these methods and focus on the results of these simulations.