Presenting Circular Gravitational Fields: A Numerical Exploration around Rotating Black Holes

We present a novel theoretical framework, Circular Gravitational Fields (CGF), which extends the gravitomagnetic analogy in general relativity by proposing that mass-energy currents generate a circular component of the gravitational field. Our formulation provides a geometrically motivated coupling between this circular field and spacetime curvature through the Ricci tensor, maintaining consistency with established gravitational physics while predicting potentially observable deviations in strong-field regimes. Using the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formalism, we perform numerical simulations of rotating black holes to explore CGF behavior in strong gravitational fields. We compare CGF predictions for key observables, including frame-dragging effects and gravitational wave signatures, with solutions to Einstein’s equations. Our approach maintains consistency with current observational constraints from gravitational wave observations [1] and cosmological surveys [2], while offering new insights into the quantum nature of spacetime. The framework makes specific predictions for next-generation experiments including Euclid, the Einstein Telescope [3], and pulsar timing arrays, providing multiple avenues for empirical verification of these fundamental ideas about the nature of time and reality.