Analytical calculation of self-force effects on a scalar particle in an eccentric orbit around a Schwarzschild black hole

Abstract In this work, we analytically investigate the effects of the scalar self-force exerted by a massless scalar field on a particle in a slightly eccentric orbit around a Schwarzschild black hole. By solving the Klein–Gordon equation in the curved spacetime background, using a combination of post-Newtonian (PN) expansion, and small-eccentricity approximation, we derive explicit expressions for the self-force components at the particle location, as well as for the associated energy and angular momentum fluxes. Our results are valid up to sixth PN order and fourth order in eccentricity ( e 4 ). We compare asymptotic fluxes with those obtained in Trestini (2024 Phys. Rev. D 109 104003) for scalar–tensor (ST) theories. Once the relation between the two approaches has been established, we find perfect agreement by fixing the asymptotic value of the scalar field in ST theory φ 0 = 1.