Three-flavor gravitationally induced neutrino oscillations and the solar neutrino problem

Some implications of the proposal that flavor nondiagonal couplings of neutrinos to gravity might resolve the solar neutrino problem are considered in the context of three neutrino flavors. The two-flavor model is discussed as a limiting case of the full three-generation mechanism, and the behavior of the ${\nu }_e$ survival probability for various values of the three-flavor parameters is studied. Overlapping allowed SNU regions are obtained for the neutrinos which most likely contribute to the observed solar neutrino deficiency, and the effects of the addition of a third flavor are discussed. The extension to a three-generation framework is found to yield a greater allowed region of parameter space, suggesting that gravitationally induced neutrino oscillations remain a viable explanation of the solar neutrino problem.