Analytical self-force on scalar particle in eccentric orbits around a Schwarzschild black hole

2025/06/02 by Capozziello, Salvatore, Menadeo, Nicola, Usseglio, Davide · 1 citation
#FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.2506.01693

Abstract

In this work, we analytically investigate the effects of 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 post-Newtonian (6PN) order and fourth order in eccentricity (e⁴). We compare asymptotic fluxes with those obtained in arXiv:2401.06844 for scalar-tensor (ST) theories. Once that the relation between the two approaches has been established, we found perfect agreement by fixing the asymptotic value of the scalar field in ST theory ϕ₀ = 1.

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