The gravitational waveforms associated with coalescing binary neutron stars and black holes are increasingly well understood, and will be a powerful tool to test the genuinely strong-field dynamics of General Relativity (GR). We present TIGER, a Bayesian inference framework which tests the consistency of coefficients appearing in the waveforms with the predictions made by GR, without relying on any specific alternative theory of gravity. TIGER is suitable for low signal-to-noise ratio events through the construction of multiple subtests, most of which involve only a limited number of coefficients. It also naturally allows for the combination of information from multiple sources to increase one’s confidence in GR or a violation thereof. In the case of inspiraling binary neutron stars, TIGER has been fully implemented as a data analysis pipeline in the LIGO Algorithms Library. We show results for a range of numerical experiments in simulated stationary and Gaussian noise that follows the expected Advanced LIGO and Virgo noise curves. Potential concerns are addressed, such as differences between waveform approximants, the effects of instrumental calibration errors, tidal deformability of the neutron stars, and the influence of spins. Finally, we discuss possible ways of extending TIGER to the coalescence of binary black holes.
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