Light Curve and Hardness Tests for Millilensing in GRB 950830, GRB 090717A, and GRB 200716C

To show an internal signature of gravitational lensing, two different temporal sections of a single gamma-ray burst (GRB) must be statistically similar. Here two straightforward gravitational lensing tests are defined and applied: a light-curve similarity test and a hardness similarity test. Gravitational millilensing has been claimed to be detected within several individual GRBs that contain two emission episodes separated by a time delay. However, our analyses indicate that none of those claims clearly satisfy both tests. The hardness similarity test performed on GRB 950830 and GRB 090717A found that the ratio between the second and the first emission episodes in each energy channel differed from the same ratio averaged over all detected energy channels at above the 90 percent confidence level. Also, a light curve similarity test performed on GRB 950830, GRB 090717A, and GRB 200716C separately, found that it is unlikely that the two emission episodes in each GRB were drawn from a single parent emission episode for that GRB, with differences at the 3.0 sigma, 8.3 sigma, and 8.3 sigma confidence levels respectively.