Analytic Kludge Waveforms for Extreme Mass Ratio Inspirals of Charged Object around Kerr-Newman Black Hole

TL;DR

This paper develops analytic waveform models for charged extreme mass ratio inspirals around Kerr-Newman black holes, revealing how small charges influence gravitational wave signals and enabling precise parameter estimation.

Contribution

It introduces analytic-kludge waveforms for charged EMRIs, incorporating electromagnetic and metric effects, and assesses their detectability and parameter estimation accuracy.

Findings

Tiny charges produce detectable waveform imprints.

Parameter estimation can reach a precision of 10^{-5} for charges.

Charges affect the inspiral cutoff and waveform features.

Abstract

We derive the approximate, ``analytic-kludge'' (AK) waveforms for the inspiral of a charged stellar-mass compact object (CO) into a charged massive Kerr-Newman (KN) black hole (BH). The modifications of the inspiral orbit due to the charges in this system can be attributed to three sources: the electric force between the CO and the MBH, the energy flow of the dipole electromagnetic radiation, and the deformation of the metric caused by the charge of the MBH. All these are encoded explicitly in the fundamental frequencies of the orbits, which are calculated analytically in the weak-field regime. By calculating the mismatch between the waveforms for charged and neutral EMRI systems with respect to space-borne detectors TianQin and LISA, we show that tiny charges in the system can produce distinct imprints on the waveforms. Finally, we perform parameter estimation for the charges using the Fisher information matrix method and find that the precision can reach the level of $10^{-5}$ in suitable scenarios. We also study the effects of charges on the parameter estimation of charge, where the effects from the charge of the MBH can be well explained by its effects on the cutoff of the inspiral.