Theoretical Radio Signals from Radio-Band Gravitational Waves Converted from the Neutron Star Magnetic Field

Gravitational waves (GWs) can convert into electromagnetic waves in the presence of a magnetic field via the Gertsenshtein-Zeldovich (GZ) effect. The characteristics of the magnetic field substantially affect this conversion probability. This paper confirms that strong magnetic fields in neutron stars significantly enhance the conversion probability, facilitating detectable radio signatures of very high-frequency (VHF, $\left(10^6-10^{11}\mathrm{~Hz}\right)$) gravitational waves. We theoretically identify two distinct signatures using single-dish telescopes (FAST, TMRT, QTT, GBT) and interferometers (SKA1/2-MID): transient signals from burst-like gravitational wave sources and persistent signals from cosmological background gravitational wave sources. These signatures are mapped to graviton spectral lines derived from quantum field theory by incorporating spin-2 and mass constraints, resulting in smooth, featureless profiles that are critical for distinguishing gravitational wave signals from astrophysical foregrounds. FAST attains a characteristic strain bound of $h_c<10^{-23}$, approaching $10^{-24}$ in the frequency range of $1-3\mathrm{~GHz}$ with a 6-hour observation period. This performance exceeds the $5 \sigma$ detection thresholds for GWs originating from primordial black holes (PBHs) and nears the limits set by Big Bang nucleosynthesis. Additionally, projections for SKA2-MID indicate even greater sensitivity. Detecting such gravitational waves would improve our comprehension of cosmological models, refine the parameter spaces for primordial black holes, and function as a test for quantum field theory. This approach addresses significant deficiencies in VHF GW research, improving detection sensitivity and facilitating the advancement of next-generation radio telescopes such as FASTA and SKA, which feature larger fields of view and enhanced gain.