Inverse Gertsenshteǐn-Zel'dovich Effect in Time-Independent Electromagnetic Field

The inverse Gertsenshteǐn-Zel'dovich effect describes the conversion of gravitational waves into electromagnetic waves in the presence of a background electromagnetic field. This effect has primarily been studied for constant background electromagnetic fields. In this work, we develop a general formalism for calculating the components of the electric and magnetic fields induced by the passage of a gravitational wave through a spatially varying, time-independent background electromagnetic field. The formalism accommodates all six possible polarization modes of gravitational waves. We illustrate its applicability through several examples, including gravitational waves propagating through constant and spatially varying electromagnetic fields. We further investigate the electromagnetic signals generated by the passage of gravitational waves through astrophysical magnetic fields, particularly those associated with neutron stars and magnetars. By connecting gravitational waves and electromagnetic waves--two essential messengers of multi-messenger astronomy--the inverse Gertsenshteǐn-Zel'dovich effect offers a promising framework for both gravitational-wave detection and astrophysical observations. The formalism developed here may therefore find applications in the design of high-frequency gravitational-wave detectors and in the investigation of high-energy astrophysical electromagnetic signals.