  The dense environment of neutron stars makes them an excellent target for
probing dark matter interactions with the Standard Model. We study neutron star
heating from capture of inelastic dark matter, which can evade direct detection
constraints. We investigate kinematics of the inelastic scattering process
between quasirelativistic dark matter particles and ultrarelativistic targets
in neutron stars, and derive analytical expressions for the maximal mass gap
allowed for the scattering to occur. We implement them into a fully
relativistic formalism for calculating the capture rate and apply it to various
scenarios of inelastic dark matter. The projected constraints from neutron
stars can systematically surpass those from terrestrial searches, including
direct detection and collider experiments. Neutron stars can also be sensitive
to the parameter space of inelastic self-interacting dark matter. Our results
indicate that extreme astrophysical environments, such as neutron stars, are an
important target for searching dark matter.
