Presenting Circular Gravitational Fields: A Numerical Exploration Around Rotating Black Holes, Third Revision

We present a comprehensive numerical investigation of Circular Gravitational Field (CGF) theory— a novel extension of general relativity that introduces a geometric coupling between a U(1) gauge field and spacetime curvature through the Ricci tensor. Using a multi-messenger approach, we analyze data from binary black hole mergers, neutron star mergers, pulsar timing arrays, and the Event Horizon Telescope to constrain CGF parameters. Our analysis of seven LIGO/Virgo black hole merger events indicates significant evidence (combined 8.32σ) for CGF effects, most prominently in high-mass, high-spin systems like GW170729 (8.05σ). We determine the optimal CGF coupling parameter to be λ ≈ 4.19 × 10−22, which produces testable predictions for future gravitational wave observations. These findings suggest that circular gravitational fields may provide a viable extension to general relativity in strong-field regimes while maintaining compatibility with current observational constraints.