Equatorial periodic orbits and gravitational wave phenomenology around spherically-symmetric vacuum solution in Freund–Nambu scalar–tensor gravity

Abstract

We investigate test particle dynamics and gravitational wave (GW) phenomenology in an exact spherically symmetric vacuum solution of Freund–Nambu scalar–tensor gravity. This framework generalizes the Janis–Newman–Winicour (JNW) naked singularity via a geometric non-linear coupling q and a direct scalar-particle coupling

. We demonstrate that these parameters systematically modify the Innermost Stable Circular Orbit (ISCO) – which shifts inward for

$$g_s > 0$$ g s > 0

– and the Marginally Bound Orbit (MBO). Furthermore, we classify bound periodic trajectories to isolate extreme zoom–whirl orbits exhibiting intense periapsis precession. By applying the Numerical Kludge method to Extreme Mass-Ratio Inspirals (EMRIs), we reveal that scalar–tensor corrections induce a macroscopic temporal dephasing in high-frequency GW bursts, even when the orbit’s spatial topology is preserved. These unique phase shifts offer a robust diagnostic signature for future space-based observatories like LISA to probe the strong-field regime and constrain scalar–tensor extensions of general relativity.