We show how, via gravitational repulsion associated with the Schwarzschild solution to the field equations of General Relativity, the extragalactic neutrinos, IceCube-170922A and KM3-230213A, were accelerated to high energy and ultra high energy respectively. Our theory supports the presumption that a blazar is the source of IceCube-170922A. However, it does not support the presumption that a blazar is the source of KM3-230213A. On the contrary, it leads to the conclusion that the source possesses stellar mass. The muon neutrino mass has not been experimentally determined. Our theory predicts that it is in the range 0.030 to 0.092 eV, if the blazar TXS 0506+056 is the source of IceCube-170922A. If, however, the source is PKS 0502+049, then the mass of muon neutrino is:
. We also pinpoint the fallacy in the arguments of the critics of the concept of gravitational repulsion in the Schwarzschild field.
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