Analytical calculation of self-force effects on a scalar particle in an eccentric orbit around a Schwarzschild black hole
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912985925025792 |
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| author | Capozziello, Salvatore Menadeo, Nicola Usseglio, Davide |
| author_facet | Capozziello, Salvatore Menadeo, Nicola Usseglio, Davide |
| contents | 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 post-Newtonian (6PN) order and fourth order in eccentricity ($e^4$). We compare asymptotic fluxes with those obtained in arXiv:2401.06844 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 $ϕ_0 = 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_01693 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analytical calculation of self-force effects on a scalar particle in an eccentric orbit around a Schwarzschild black hole Capozziello, Salvatore Menadeo, Nicola Usseglio, Davide General Relativity and Quantum Cosmology High Energy Physics - Theory 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 post-Newtonian (6PN) order and fourth order in eccentricity ($e^4$). We compare asymptotic fluxes with those obtained in arXiv:2401.06844 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 $ϕ_0 = 1$. |
| title | Analytical calculation of self-force effects on a scalar particle in an eccentric orbit around a Schwarzschild black hole |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2506.01693 |