Investigating the relation between gravitational wave tests of general relativity

Gravitational wave observations of compact binary coalescences provide precision probes of strong-field gravity. There is thus now a standard set of null tests of general relativity (GR) applied to LIGO-Virgo detections and many more such tests proposed. However, the relation between all these tests is not yet well understood. We start to investigate this by applying a set of standard tests to simulated observations of binary black holes in GR and with phenomenological deviations from GR. We consider four types of tests: residuals, inspiral-merger-ringdown consistency, parametrized phasing (two versions), and modified dispersion relation. We also check the consistency of the unmodeled reconstruction of the waveforms with the waveform recovered using GR templates. These tests are applied to simulated observations similar to GW150914 with both large and small deviations from GR and similar to GW170608 just with small deviations from GR. We find that while very large deviations from GR are picked up with high significance by almost all tests, more moderate deviations are picked up by only a few tests, and some deviations are not recognized as GR violations by any test at the moderate signal-to-noise ratios we consider. Moreover, the tests that identify various deviations with high significance are not necessarily the expected ones. In particular, the parametrized tests recover PN test parameters much closer to zero than their true values in some cases. Additionally, we find that of the GR deviations we consider, the residuals test is only able to detect extreme deviations from GR that no longer look like binary black hole coalescences in GR. The reconstruction comparison shows more promise for detecting relatively small GR deviations in an unmodeled framework, at least for high-mass systems.