Research Opportunities
My research specialty is numerical relativity.
- Gravitation and general relativity;
- Relativistic fluid dynamics;
- Numerical methods;
- Parallel computing.
- Nonlinear equations, complexity, chaos.
General Relativity
General relativity describes gravitational phenomena geometrically as curvature in spacetime: Matter curves space, and the spacetime curvature affects matter. General relativity predicts that accelerating objects can emit gravitational radiation. While this radiation is typically extremely weak, some astrophysical systems, such as colliding black holes or neutron stars, may emit gravitational waves that we can detect on Earth. Large, kilometer scale laser interferometers, such as LIGO, are being constructed to study gravitational wave signals from these events. Unfortunately, we currently know very little about the radiation expected from the regions of spacetime with the strongest (nonlinear) gravitational fields. I study computational methods for solving the Einstein equations for these strong-field gravitational wave sources. Various projects are available to investigate black hole spacetimes, black hole formation, and properties of the Einstein equations. All projects require writing, testing, and running computer codes to investigate nonlinear gravitational phenomena. Students should plan on spending a significant amount of time learning the fundamentals of general relativity, tensor analysis and computational methods as part of their research.
Relativistic fluid dynamics
Neutron star collapse, supernovae, gamma-ray sources, etc., are some of the exciting topics in relativistic astrophysics, and the perfect fluid is the fundamental model for all of these. I study relativistic perfect fluids near black holes using computational methods. In particular, Eric Hirschmann, Steven Millward and I at BYU are studying a magnetized fluid around a black hole with computational Magneto-Hydrodynamics (MHD). Various computational projects are available in RFD and MHD, which require writing, testing and running computer programs to model relativistic fluids.
Relativistic fluid dynamics
Research with the Einstein equations and RFD requires sophisticated numerical methods and techniques (as well as cheats and tricks). Some techniques include adaptive mesh refinement (AMR), parallel computing, high-resolution shock-capturing methods for fluid equations. Some systems, such as moving black holes, may naturally be solved in multiple reference frames simultaneously. I am investigating the use of overlapping computational grids for these problems. One particular interest is combining modern fluid methods with overlapping grids.