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arXiv · 2610.26113

Periodic orbits and gravitational-wave emission from extreme-mass-ratio inspirals around rotating charged black holes in nonlinear electrodynamics

Xi Luo·Meirong Tang·Zhaoyi Xu
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Abstract

Within general-relativistic descriptions, the no-hair theorem dictates that black-hole geometries possess just three intrinsic physical quantities: mass, angular momentum, and electric charge. Black holes in nonlinear electrodynamics (NED) are equivalent to those composed of anisotropic matter and can develop "hair" structures near the event horizon, serving as ideal testbeds for modified theories of gravity. Working within Einsteinian gravitational theory, we adopt a coupling construction between gravity and NED matter, focusing explicitly on the Einstein-Euler-Heisenberg (EEH) variant with the power-index parameter fixed at s = 2. In this framework, a rotating, charged NED black hole extends the Kerr-Newman geometry with extra correction terms. Treating spin a and NED charge q as primary control variables, we examine test-particle dynamics inside extreme-mass-ratio inspiral (EMRI) configurations. We derive equatorial timelike geodesics and the effective potential. Through numerical evaluation of marginally-bound orbits (MBO) and innermost stable circular orbits (ISCO), we explore how these parameters reshape the energy-angular-momentum (E-L) phase-space. Using the (z, w, v) integer-valued orbit taxonomy, we compute the two gravitational-wave polarization modes h+ and hx via the adiabatic approximation and quadrupole radiation prescription. Larger values for a and q drive inward contraction for bound trajectories while displacing the E-L phase-space toward smaller angular-momentum values. Periodic-orbit zoom-whirl signatures grow increasingly prominent, while larger parameter values shorten the waveform periods and enhance signal amplitudes. Our results provide theoretical support for space-borne gravitational-wave observatories including LISA and TianQin, enabling prospects for discriminating NED black-hole spacetimes and performing observational checks on the no-hair theorem.

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Xi Luo, Meirong Tang, Zhaoyi Xu. 2026-10-19. Periodic orbits and gravitational-wave emission from extreme-mass-ratio inspirals around rotating charged black holes in nonlinear electrodynamics. https://arxiv.org/abs/2610.26113

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