Techniques for evolving Einstein's equations

Louisiana State University, Baton Rouge LA

Investigators

Abstract

This award supports a research program to use analytical and numerical techniques in the study of sources of gravitational waves with emphasis on binary black hole collisions. Gravitational wave detectors such as LIGO urgently need the gravitational waveforms that would be obtained from the successful numerical simulation of these systems. These simulations are of a complexity such that special advances in techniques and infrastructure for the numerical solution of Einstein's equations are needed. The project includes further development and application to binary black hole simulations of state-of-the-art techniques from computational physics and applied mathematics. The numerical solution of Einstein's equations has historically posed unique, problems associated with features inherent to Einstein's theory, such as gauge conditions and constraint violations. As part of this project novel techniques whose goal is to deal with these unique problems will be developed or extended and applied to binary black hole collisions. At the analytical level the project includes development and application of techniques to deal with constraint instabilities, boundary conditions for Einstein's equations, and coordinate conditions. At the discrete level it includes development and application techniques for multi-patch simulations, high order methods, methods for matching Einstein's equations to perturbative and other modules, constraint projection and variational integrators. The development of the necessary computational infrastructure to apply these techniques will be done in close collaboration with the Cactus development group at LSU. LSU provides an unique assembly of experts in numerical relativity and scientific computing whose expertise can be leveraged by this project.