Assessing biases in testing general relativity due to Type II lensing of binary black hole signals

The detection of gravitational waves (GW) originating from binary black hole (BBH) coalescences has emerged as a powerful tool for probing the strong-field dynamics of general relativity (GR). In this study, we investigate biases from strong gravitational lensing on tests of GR with GW signals, since this effect is not accounted for in the current implementation of these tests. In the geometric optics approximation, strong lensing produces three image types (Type I, Type II, and Type III). Our focus is on Type II signals, where the introduced phase shift is non-degenerate with the parameters of quasicircular binaries if there are non-negligible higher modes and/or precession. We assess the response of four standard tests of GR to simulated Type II lensed BBH signals. Specifically, we consider a test for consistency between the low- and high-frequency parts of the signal, two tests that constrain parameterized modifications to the signal phase (e.g., in the post-Newtonian coefficients), and a test for dispersive propagation effects. We investigate the binary parameters for which Type II lensing leads to significant false GR deviations when observed with near-future ground-based GW detectors.