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The neutrino–antineutrino annihilation into electron–positron pairs near the surface of compact general relativistic stars could play an important role in supernova explosions, neutron star collapse, or for close neutron star binaries near their last stable orbit. General relativistic effects increase the energy deposition rates due to the annihilation process. We investigate the deposition of energy and momentum due to the annihilations of neutrinos and antineutrinos in the equatorial plane of the rapidly rotating neutron and quark stars, respectively. We analyse the influence of general relativistic effects, and obtain the general relativistic corrections to the energy and momentum deposition rates for arbitrary stationary and axisymmetric space–times. We obtain the energy and momentum deposition rates for several classes of rapidly rotating neutron stars, described by different equations of state of the neutron matter, and for quark stars, described by the Massachusetts Institute of Technology bag model equation of state and in the colour‐flavour‐locked phase, respectively. Compared to the Newtonian calculations, rotation and general relativistic effects increase the total annihilation rate measured by an observer at infinity. The differences in the equations of state for neutron and quark matter also have important effects on the spatial distribution of the energy deposition rate by neutrino–antineutrino annihilation.

Electron–positron energy deposition rate from neutrino pair annihilation in the equatorial plane of rapidly rotating neutron and quark stars