Eloisa Bentivegna - Graduate Student
301C Whitmore Laboratory
Gauge Conditions for Binary Black Hole Coalescence
My interests are currently focused on Numerical Relativity, the branch of General Relativity that is responsible for the implementation and the analysis of different computational algorithms to solve Einstein's equations. Due to the deep nonlinearity of this system of equations, the superposition principle is no longer applicable, and the construction of articulate physical solutions can no longer proceed from the knowledge of the few analytically-known solutions. The attention and effort that are currently dedicated to the detection of gravitational waves have also enriched this field with an additional goal: producing a theoretical counterpart for gravitational wave astronomy observations. The vast majority of studies in Numerical Relativity today is thus centered around astrophysical sources of gravitational radiation, such as binary systems of inspiraling black holes or other compact objects. Numerical studies are meant to simulate such systems and extract the corresponding waveforms, building up a theoretical wave template collection for the detection of gravitational waves.
Aside from the standard issues that pertain to every sort of computational work (speed vs. accuracy tradeoff, stability matters, and the like), the numerical simulation of general relativistic systems presents its own characteristic open questions. For instance, there is no univocal concept of time evolution in a generic, four-dimensional spacetime. All numerical simulations begin with the choice of a time direction and a corresponding foliation of the spacetime into a set of three-dimensional spatial hypersurfaces, parametrized by a constant time value. The specification of spatial coordinates on those hypersurfaces implies another arbitrary choice, and both of these have proven to affect dramatically the stability of the evolved systems. In a way, this can be regarded as an extension of the time-old problem of adapting the coordinates to the symmetries of a system, in order to get rid of spurious dynamics and obtain the simplest possible physical description. Other open questions include the construction of accurate initial data to initialize the evolution and the numerical handling of the spacetime singularities generated by gravitational collapse.
I am currently involved, as a developer of Penn State's MAYA code, in the study of the problem of coordinates. In the past few months, I have investigated several sets of gauge conditions, coding them into MAYA and running tests to evaluate their numerical performance. The individuation of an adapted coordinate system will then aid in the simulation, eliminating the unphysical degrees of freedom and retaining only the interesting physical evolution that is responsible for the production of gravity waves.