Light curve and hardness tests for millilensing in GRB 081122A, GRB 081126A, GRB 110517B, and GRB 210812A

Analyses are given on four recent gravitational millilensing claims on gamma-ray bursts (GRBs): GRB 081122A, GRB 081126A, GRB 110517B, and GRB 210812A. Two tests, a light curve similarity test and a hardness similarity test, compare different temporal sections of a single GRB to see if they are statistically similar. The hardness similarity test shows that the ratio between the second and the first emission episodes in each energy channel differed from the same ratio averaged over all energy channels at above 90 per cent confidence level in GRB 081122A. Additionally, the light curve similarity test applied to GRB 081122A, GRB 081126A, and GRB 110517B separately indicated a high likelihood that the two emission episodes in each GRB were not from the same parent emission episode. This conclusion was reached with confidence levels of 4.8 sigma for GRB 081122A, 3.08 sigma for GRB 081126A, and 8.45 sigma for GRB 110517B. However, these tests did not detect a significant difference between the pulses of GRB 210812A. Consequently, our results suggest that while GRB 210812A could not be conclusively ruled out, the other three GRBs do not show clear evidence of millilensing.