Gravitational radiation reaction around a static black hole surrounded by a Dehnen type dark matter halo

We consider the motion of a particle in the geometry of a Schwarzschild-like black hole embedded in a dark matter (DM) halo with Dehnen type density profile and calculate the orbital periods along with the evolution of the semi-latus rectum and eccentricity for extreme mass ratio inspirals (EMRIs). Such a system emits gravitational waves (GWs), and the particle's orbit evolves under radiation reaction. We also consider the effects of dynamical friction and accretion of DM on the orbital parameters. We find that the eccentricity and semi-latus rectum decrease faster with respect to the case in which EMRI is in empty spacetime.