Determining the minimal covering set of parameter spaces for phenomenological gravitational waveforms

Abstract

Gravitational wave observatories are now trying to detect gravitational waves, ripples in space time predicted by Einstein’s theory of General Relativity, from sources such as merging binary star and black hole systems. Numerical relativists create template banks of gravitational waves from merging black hole binaries in an effort to confirm a gravitational wave detection by solving Einstein’s field equations. These waveforms are then compared to the raw data collected by gravitational wave detectors. Since it is computationally expensive to produce the full numerical relativity waveforms, theorists have created approximation techniques called phenomenological waveforms, in which analytical functions approximate the numerical solutions over a finite space of parameters. It is computationally expensive to match the waveform template banks to the data from the observatories. In an effort to minimize the number of waveforms in the template banks, I determine the minimal covering set of the parameter space for non-spinning binary black hole phenomenological waveforms. This is accomplished by marching through a very fine mesh of the parameter space, ensuring that the match between adjacent waveforms is above a given threshold. I determine this minimal covering set for the non-spinning case and discuss how to generalize the program to the full spinning case.