GRAVITATIONAL LENSING, TIME-DELAY, AND GAMMA-RAY BURSTS

The probability distributions of time delay in gravitational lensing by point masses and isolated galaxies (modeled as singular isothermal spheres) are studied. We find that for point lenses (all with the same mass M*), the probability distribution is broad, and with a peak at DELTA-t almost-equal-to 50 s (M*/10(6) M.); for singular isothermal spheres, the probability distribution is a rapidly decreasing function with increasing time delay, with a median DELTA-t almost-equal-to 1 h-1 month, and its behavior depends sensitively on the luminosity function of galaxies. The present simplified calculation is particularly relevant to the gamma-ray bursts if they are of cosmological origin. The frequency of "recurrent" bursts due to gravitational lensing by galaxies is probably between 0.05% and 0.4%. BATSE on Gamma Ray Observatory may observe several such lensing events. BATSE may also provide the most stringent limit on the mass density of cosmological massive black holes. Gravitational lensing therefore can be used as a test of the cosmological origin of gamma-ray bursts.