Neutrino pair annihilation ($$\nu {\bar{\nu }}\rightarrow e^-e^+$$) in the presence of quintessence surrounding a black hole

Quintessence fields, introduced to explain the speed-up of theUniverse, might affect the geometry of spacetime surrounding black holes, as compared to the standard Schwarzschild and Kerr geometries. In this framework, we study the neutrino pairs annihilation into electron-positron pairs (nu(nu) over bar -> e(-) e(+)) near the surface of a neutron star, focusing, in particular, on the Schwarzschild-like geometry in presence of quintessence fields. The effect of the latter is to increase the photon-sphere radius (R-ph), increasing in such a way the maximum energy deposition rate near to R-ph. The rate turns out to be several orders of magnitude greater than the rate computed in the framework of General Relativity. These results might provide a rising in the GRBs energy emitted from a close binary neutron star system and might be used to constraints the parameters of the quintessence model. Finally we theoretically study the effects of rotation on the neutrino energy deposition.