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We discuss the formation of dark compact objects in a dark matter environmentin view of the possible mass dependence of pulsars on the distribution of darkmatter in the Galaxy. Our results indicate that the pulsar masses shoulddecrease going towards the center of the Milky Way due to dark matter capture,thus becoming a probe for the existence and nature of dark matter. We thuspropose that the evolution of the pulsar mass in a dark matter rich environmentcan be used to put constraints, when combined with future experiments, on thecharacteristics of our Galaxy halo dark matter profile, on the dark matterparticle mass and on the dark matter self-interaction strength.

Can Pulsars in the inner parsecs from Galactic Centre probe the existence of Dark Matter?