Gamma ray signals from annihilating dark matter in curved spacetime

Abstract

In order to investigate gamma ray signals from dark matter originating from close to the black hole at the galactic center, we investigate the effects of general relativity on such a signal. The expression for the photon flux in flat spacetime is derived, and then generalized to take into account the geodesics of the photons, as well as the gravitational redshift. We calculate $J(\psi)$ in the Schwarzschild spacetime, and find the photon flux for the case where the particles annihilate at rest. It is found that these relativistic considerations could potentially alter the spatial signal, but mostly for angular resolutions too small for present day detectors, and only in a region heavily influenced by uncertainties in the dark matter halo. The spectral signal shows a redshift of $\Delta x=0.1$, which should in principle be detectable if we had a better understanding of the background processes. The spectrum also shows potential features for smaller $x$, though these features might be because of numerical errors.