 Solution

Gravitational waves can exhibit interference. In linearized gravity, overlapping strains add, so coherent contributions can enhance or cancel the measured response. Independent astrophysical sources generally have unrelated phases and average to a stochastic background rather than stable fringes. More plausible coherent paths arise when gravitational lensing sends different parts of the same signal to the detector with different delays; fringes require sufficient overlap and coherence. The relevant quadratic radiative energy flux contains the cross terms even though the leading wave equation is linear.