Notes on the integration of numerical relativity waveforms

Abstract

The primary goal of numerical relativity is to provide estimates of the wave strain, h, from strong gravitational wave sources, to be used in detector templates. The simulations, however, typically measure waves in terms of the Weyl curvature component, ψ_4. Assuming Bondi gauge, transforming to the strain h reduces to integration of ψ_4 twice in time. Integrations performed in either the time or frequency domain, however, lead to secular nonlinear drifts in the resulting strain h. These nonlinear drifts are not explained by the two unknown integration constants which can at most result in linear drifts. We identify a number of fundamental difficulties which can arise from integrating finite length, discretely sampled and noisy data streams. These issues are an artifact of post-processing data. They are independent of the characteristics of the original simulation, such as gauge or numerical method used. We suggest, however, a simple procedure for integrating numerical waveforms in the frequency domain, which is effective at strongly reducing spurious secular nonlinear drifts in the resulting strain.

Additional details