Gravitomagnetic Scalar Response: A Transient Phase Transition in Strong-Field Gravity

Abstract Background. The complex morphologies observed in recent gravitational wave detections suggest that the spacetime fabric may undergo dynamical modifications during the extreme conditions of binary black hole mergers. Aim. We propose the Gravitomagnetic Scalar Response (GSR) framework, a novel effective field theory of gravity featuring a transient, source-dependent phase transition driven by rapidly varying gravitomagnetic stress. Methods. The transition is governed by a scalar order parameter coupled to the temporal variation of the gravitomagnetic invariant I B via a non-linear activation function. To cure the Ostrogradsky instability inherent in the higher-derivative trigger, we introduce a response scalar field that regularises the action and compute the scalar kinetic matrix explicitly.Results. We prove that the GSR theory strictly recovers General Relativity in all stationary and weak-field regimes, including isolated black holes and cosmological expansion, confining novel phenomenology exclusively to the peak of binary mergers. The free quadratic scalar sector is ghost-free provided the phase transition is sufficiently smooth, a condition physically required by finite-energy considerations. Conclusions. The GSR framework predicts specific observational signatures for next-generation detectors, including transient polarization-dependent dispersion, overtone anomalies in the early ringdown, and threshold-driven multi-peak structures in the merger strain of precessing binaries.