Numerical estimation of the escaping flux of massless particles created in collisions around a Kerr black hole

The geodesics of massless particles produced in collisions near a rotating black hole are solved numerically and a Monte Carlo integration of the momentum distribution of the massless particles is performed to calculate the fraction that escape the black hole to infinity. A distribution of in falling dark matter particles, which are assumed to annihilate to massless particles, is considered and an estimate of the emergent flux from the collisions is made. The energy spectrum of the emergent particles is found to contain two Lorentz shifted peaks centered on the mass of the dark matter. The separation of the peaks is found to depend on the density profile of the dark matter and could provide information about the size of the annihilation plateau around a black hole and the mass of the dark matter particle.