Black Holes: Excision and Matter Interactions

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Numerical solutions of Einstein's equations of general relativity provide the most promising means to understand phenomena associated with strong gravitational fields such as those expected from colliding black holes. This award supports development methods to solve Einstein's equations for black holes using excision to eliminate the black hole interior from the computational domain and a magnetic fluid to model matter interactions in the environment of the black hole. Techniques to be explored and developed include the use of potentially more efficient and stable second-order spatial derivatives in generalized harmonic coordinates, excision with multiple coordinate patches for dynamic spacetimes, and application of numerical methods for conservation equations, such as those for the magnetic fluid, for domains with multiple coordinate patches. Promising discretization schemes and boundary conditions for computational stability will be studied. Initial tests will solve the Einstein equations for axisymmetric black hole spacetimes, eventually leading to head-on collisions of black holes. Astrophysical sources of gravitational radiation must be better understood to fully exploit the gravitational wave data expected from ground-based detectors such as LIGO and the space-based LISA. The numerical techniques developed in this project will have a broader impact on astrophysical fluid dynamics and more generally in computational science, especially in applications where boundaries must be accurately modeled. Furthermore, this project provides significant research opportunities to undergraduate students at Brigham Young University as well as opportunities for them to present scientific results at professional conferences.