  We present our studies on the neutrino pairs annihilation into
electron-positron pairs ($\nu{\bar \nu}\to e^-e^+$) near the surface of a
neutron star in the framework of extended theories of gravity. The latter
modifies the maximum energy deposition rate near to the photonsphere and it
might be several orders of magnitude greater than that computed in the
framework of General Relativity. These results provide a rising in the
Gamma-Ray Bursts energy emitted from a close binary neutron star system and
might be a fingerprint of modified theories of gravity, changing our view of
astrophysical phenomena.
