Gravitational-wave imprints of Kerr–Bertotti–Robinson black holes: frequency blue-shift and waveform dephasing

Abstract We investigate the orbital dynamics and gravitational wave signatures of neutral extreme mass ratio inspirals (EMRIs) in the spacetime of a Kerr black hole immersed in an asymptotically uniform magnetic field, described by the exact Kerr–Bertotti–Robinson (Kerr–BR) solution (Podolsky and Ovcharenko in Phys Rev Lett 135:181401, 2025). Unlike the widely used Kerr–Melvin metric, the Kerr–BR solution is of algebraic type D, allowing for a rigorous analysis of geodesics and possessing a clear asymptotic structure. By analyzing the Innermost Stable Circular Orbit (ISCO), we confirm that the external magnetic field consistently pushes the ISCO to larger radii. However, contrary to Newtonian intuition, this radial expansion is accompanied by a systematic magnetically induced hardening of the spectrum, where the ISCO frequency is blue-shifted relative to the vacuum case. Notably, in the strong-field regime, we identify a non-monotonic frequency evolution, where the orbital frequency initially decreases before rising rapidly near the horizon, fundamentally altering the chirp character. We further demonstrate that retrograde orbits are significantly more sensitive to magnetic fields than prograde orbits, leading to frequency crossover phenomena where magnetic effects can invert the usual spin-frequency hierarchy. Finally, employing a semi-analytic adiabatic evolution scheme, we quantify the dephasing accumulated during the final year of inspiral. Our results demonstrate that space-borne detectors like LISA can distinguish magnetic environments from vacuum spacetimes for field strengths as low as $$B \sim 10^{-4}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>B</mml:mi> <mml:mo>∼</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> , suggesting that environmental magnetic fields could introduce systematic biases in parameter estimation if not properly modeled.