{"paper":{"title":"Theoretical Aspects of Direct Waves in Kerr Black Holes: Pole-Splitting Method for Ringdown Analysis","arxiv_id":"2609.11908","primary_cat":"gr-qc","submitted_at":"2026-09-10T17:56:30+00:00","version_compiled":"v2"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v2","sentences":[{"i":0,"p":0.98,"id":"s0","own":true,"role":"contribution","text":"We formulate the theoretical aspects of direct waves (DWs) in the case of extreme-mass merger.","hedge":{"p":0.98,"label":"asserted"},"own_p":0.91,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.02,"limitation":0.0,"future_work":0.0,"contribution":0.98,"interpretation":0.0}},{"i":1,"p":0.86,"id":"s1","own":false,"role":"background","text":"A DW is a source-driven waveform characterized by a complex frequency $\\omega_{\\rm G}$, which reflects the orbital motion of the particle in the vicinity of the black hole, including a part of the orbit inside the ergoregion: its real part is governed by frame dragging and its imaginary part by the redshift of the source.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.16,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.07,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.01,"background":0.86,"limitation":0.0,"future_work":0.0,"contribution":0.11,"interpretation":0.01}},{"i":2,"p":0.77,"id":"s2","own":true,"role":"method","text":"Using the Green's function technique, we derive the source-driven frequency $\\omega_{\\rm G}$, describe its screening by the potential barrier, and discuss its relation to dynamically excited quasinormal modes (QNMs).","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.77,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.23,"interpretation":0.0}},{"i":3,"p":0.76,"id":"s3","own":true,"role":"method","text":"We then introduce a pole-splitting method that divides the full waveform into a QNM-pole sector and a non-QNM sector.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.94,"main_claim_p":0.07,"quantitative":false,"quantitative_p":0.07,"role_probabilities":{"gap":0.0,"method":0.76,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.24,"interpretation":0.0}},{"i":4,"p":0.7,"id":"s4","own":false,"role":"method","text":"Unlike QNM filtering, which multiplies the waveform spectrum by a filter function and thereby deforms it through a frequency-dependent time shift (i.e., group delay), our pole-splitting method merely divides the transfer function into pole and non-pole parts, separating the full waveform.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.48,"main_claim_p":0.09,"quantitative":false,"quantitative_p":0.39,"role_probabilities":{"gap":0.0,"method":0.7,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.27,"interpretation":0.03}},{"i":5,"p":0.94,"id":"s5","own":true,"role":"result","text":"Simulating a quasi-circular plunge into a Kerr black hole with medium and rapid spins, we find that the frequency and decay rate of the non-pole sector in the dominant mode, $\\ell = m = 2$, evolve consistently with $\\omega_{\\rm G}$-or with its screened counterpart $\\omega_{\\rm screen}$-establishing the DW as a probe of the ergoregion and of the redshift effect around a black hole.","hedge":{"p":0.96,"label":"asserted"},"own_p":0.96,"main_claim_p":0.76,"quantitative":true,"quantitative_p":0.6,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.94,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.06}}]},"compiled":{"main_claim":{"p":1.0,"text":"Simulating a quasi-circular plunge into a Kerr black hole with medium and rapid spins, we find that the frequency and decay rate of the non-pole sector in the dominant mode, $\\ell = m = 2$, evolve consistently with $\\omega_{\\rm G}$-or with its screened counterpart $\\omega_{\\rm screen}$-establishing the DW as a probe of the ergoregion 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