Jin-Lu Hu, Xin-Dong Du, Peng-Cheng Li, Tieguang Zi

We investigate whether weak near-zone magnetic fields can leave observable imprints on extreme-mass-ratio inspiral (EMRI) waveforms. The central massive black hole is modeled by the magnetized Schwarzschild, or Ernst, solution, and the secondary compact object is treated as a neutral point particle on equatorial circular geodesics. We compute the magnetic corrections to the circular-orbit quantities and the innermost stable circular orbit, and then evolve the inspiral using a hybrid, source-corrected Regge--Wheeler--Zerilli approximation, in which the Schwarzschild wave-propagation potentials are kept fixed while the source is evaluated on the magnetized orbit. For a fiducial system with \(M=10^6M_\odot\) and \(μ=10M_\odot\), a field strength \(B\simeq 4\times10^{-5}M^{-1}\), corresponding to \(B_{\rm phys}\sim10^9\,{\rm G}\), produces a one-year dephasing of about \(1.3\) rad and reaches the adopted LISA-noise-weighted mismatch threshold. Our results suggest that EMRIs can in principle probe extremely strong near-zone magnetic fields, whereas ordinary magnetic environments around massive black holes are likely too weak to produce detectable effects within the present approximation.