{"paper":{"title":"Analytical Fluxes from Generic Schwarzschild Geodesics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A Chebyshev expansion of radiation coefficients yields analytic gravitational-wave fluxes for eccentric Schwarzschild geodesics.","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Chris Kavanagh, Majed Khalaf, Ofri Telem","submitted_at":"2026-05-13T17:59:59Z","abstract_excerpt":"We present an analytic method for computing gravitational-wave fluxes from bound Schwarzschild geodesics with arbitrary eccentricity. Our approach systematically expands the Fourier coefficients of the emitted radiation in a Chebyshev basis, allowing them to be reduced to sums of Keplerian-like Fourier coefficients previously derived in the Quantum Spectral Method. Because the construction does not rely on a small-eccentricity expansion, it applies to a broad range of bound eccentric orbits. As an illustration, we implement the method using a $15$PN-expanded input and find that it reproduces t"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"we implement the method using a 15PN-expanded input and find that it reproduces the total flux for the case (p,e)=(12.5,0.5) to relative accuracy 10^{-5}, while for the stronger-field case (p,e)=(10,0.8) it yields weighted mode-by-mode errors below 10^{-6} for the selected dominant modes analyzed.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The Chebyshev expansion of the radiation Fourier coefficients converges rapidly enough for generic bound geodesics when the input is a 15PN series; this is assumed rather than proven for all eccentricities and field strengths.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A Chebyshev-basis expansion reduces gravitational-wave fluxes from arbitrary-eccentricity bound Schwarzschild geodesics to sums of previously derived Keplerian Fourier coefficients, achieving 10^{-5} relative accuracy on total flux for tested orbits.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A Chebyshev expansion of radiation coefficients yields analytic gravitational-wave fluxes for eccentric Schwarzschild geodesics.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"875d19066e9be08c7ffa3eef5fcbd8f6fd3bf6a8bbadf9914d55d3cd58b3e890"},"source":{"id":"2605.13847","kind":"arxiv","version":1},"verdict":{"id":"6a51ac39-9ccb-4edb-99be-22f665485df6","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T17:35:30.102768Z","strongest_claim":"we implement the method using a 15PN-expanded input and find that it reproduces the total flux for the case (p,e)=(12.5,0.5) to relative accuracy 10^{-5}, while for the stronger-field case (p,e)=(10,0.8) it yields weighted mode-by-mode errors below 10^{-6} for the selected dominant modes analyzed.","one_line_summary":"A Chebyshev-basis expansion reduces gravitational-wave fluxes from arbitrary-eccentricity bound Schwarzschild geodesics to sums of previously derived Keplerian Fourier coefficients, achieving 10^{-5} relative accuracy on total flux for tested orbits.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The Chebyshev expansion of the radiation Fourier coefficients converges rapidly enough for generic bound geodesics when the input is a 15PN series; this is assumed rather than proven for all eccentricities and field strengths.","pith_extraction_headline":"A Chebyshev expansion of radiation coefficients yields analytic gravitational-wave fluxes for eccentric Schwarzschild geodesics."},"references":{"count":38,"sample":[{"doi":"","year":null,"title":"The latter are crucial to ensure convergence over the entire intervalr p ≤r≤ ra","work_id":"4a4212c6-e706-4c50-990a-7dc0df45e6e1","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"we showed how relativistic Keplerian Fourier ele- ments, computed using (13), can be analytically contin- ued to the unbound regime and benchmarked against post-Minkowski/post-Newtonian computations. 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