Project: 3D Gravitational Waves
Project: 3D Gravitational Waves Using the same 3D numerical codes developed for evolving 3D black holes, we are evolving pure gravitational wave spacetimes (for a brief explanation of gravitational waves, see the exhibit Ripples in Spacetime ). This is neccessary step in the Grand Challenge Project, where we hope to be able to evolve 2 inspiralling black holes that are continuously radiating gravitational waves. Because of the complexity of Einstein's equations, most of the work done on gravitational waves in the past, has assumed special symmetries. We can now evolve solutions with no special symmetries. We have evolved many different types of waves, and hope to explore such events as waves colliding and forming black holes, and search for the existence of a 3D gravitational soliton.
We have recently finished a study of small amplitude waves. We evolved these waves using the fully nonlinear Einstein equations, and compared them to the analytic solutions given by the linearized Einstein equations. We discovered a regime of small amplitude waves which although expected to behave linearly, differed significantly from the linearized solutions. These nonlinear effects, manifested themselves as coordinate motion, although the underlying geometry of the spacetime was still behaving linearly (see the preprint of this paper The Near-Linear Regime of Gravitational Waves in Numerical Relativity ).We have also used gravity waves as a testbed in some of our work exploring gauge conditions in numerical relativity (see Coordinate Conditions and Their Implementation in 3D Numerical Relativity ). The goal of this work is to be able to control the motion of coordinate degrees of freedom in GR, so as to be able to provide long stable numerical simulations. The magnitude of this coordinate motion is greatly increased in 3D, since we make no special assumptions on our coordinate conditions. This was previously unexpected, and partially discovered through our work above.
See the G code project or the H code project for a description of the codes we are using.