This award supports a variety of theoretical and computational problems involving Einstein's general theory of relativity. Computational techniques will be developed in which black hole interiors are replaced with artificial data to help create more efficient and flexible numerical algorithms. New formulations of the Einstein evolution equations will be studied with the goal of developing more accurate numerical methods. A new class of initial conditions for black hole simulations will be developed, which should eliminate an important source of error in black hole simulations.
Theoretical predictions of gravitational waveforms are needed to maximize the scientific output of ground based gravitational wave detectors, such as LIGO, as well as the proposed space based LISA detector. Theoretical and numerical relativity plays a central role in these predictions. This work is part of a worldwide effort to bring gravitational wave detection into the mainstream of astrophysics research. It will open a new window on the Universe. This work will provide students with valuable skills in computational science and mathematics as well as physics.
The NSF funded LIGO detectors, which are now in operation, are designed to detect the gravitational waves emitted from violent cosmological events, such as the collision of two black holes. A successful detection will rely on a detailed understanding of the gravitational wave signal, which in turn depends on detailed theoretical and computer modeling. The work completed under this award has helped to clarify and extend many of the techniques used in computer modeling of black holes. In particular, the completed work has shown the following. (1) In a computer model, the interior of a black computer can be replaced with artificial material without affecting the prediction of the physical gravitational waves that LIGO will detect. (2) The way in which the Einstein equations are expressed in many computer codes (the "BSSN formulation") can be generalized to allow for arbitrary coordinate systems. ???(3) An alternative expression of the Einstein equations (the "generalized harmonic formulation") can be given a sound mathematical foundation, which should allow for future theoretical and computational advances. (4) A deeper understanding of the "puncture method" has been achieved. The puncture method is a common technique used in numerical simulations to handle the mathematical singularity of a black hole. ????(5) The puncture method has been extended to include black holes in higher dimensions, which opens the door for further interesting theoretical developments.
