The neutrino pair annihilation around a massive source with an f(R) global monopole

In this work we investigate the neutrino pair annihilation around a gravitational object involving an $f(R)$ global monopole. We derive and calculate ratio $\frac{\dot{Q}}{\dot{Q_{Newt}}}$ meaning that energy deposition per unit time is over in Newtonian case. It found more deviation from general relativity leads to set free with greater value. should also be pointed out existence of monopole makes sharp increase $\frac{\dot{Q}}{\dot{Q_{Newt}}}$, causing heavier gamma-ray burst. discuss derivative $\frac{d\dot{Q}}{dr}$ as function radius $r$ star show similar characters considerable modification Einstein's gravity unified theory order will raise amount greatly. The stellar body can well qualified source bursts. Moreover, select factor $\psi_{0}$ comparable accelerating universe while regulate parameter $\eta$ for make curves coincide results astronomy. possible probe astrophysical observations.