Analytic kludge waveforms for extreme-mass-ratio inspirals of a charged object around a Kerr-Newman black hole

We derive the approximate "analytic-kludge" waveforms for the inspiral of a charged stellar-mass compact object (CO) into a charged massive Kerr-Newman black hole. 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 massive black holes (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 extreme-mass-ratio inspirals 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.