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

TL;DR

This paper analyzes how magnetic fields affect the gravitational wave signals of extreme mass ratio inspirals around Kerr black holes, revealing frequency shifts and waveform dephasing that could impact LISA observations.

Contribution

It provides a detailed analysis of magnetic field effects on EMRI dynamics and gravitational wave signatures using the Kerr-Bertotti-Robinson spacetime, highlighting observable environmental influences.

Findings

Magnetic fields push the ISCO to larger radii and cause frequency blue-shifts.

Non-monotonic frequency evolution occurs in strong magnetic fields, altering chirp signals.

LISA can detect magnetic environments as weak as B ~ 10^{-4}, affecting parameter estimation.

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~\cite{Podolsky:2025tle}. 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 $B \sim 10^{-4}$, suggesting that environmental magnetic fields could introduce systematic biases in parameter estimation if not properly modeled.