Flux Memory Corrections to Hawking Radiation from Nonlocal Gauge Phases

Gauge-theoretic constructions based on null Lagrangians and exact differential forms provide an elegant route to derive dynamical equations from symmetry principles. However, such constructions implicitly assume that the relevant gauge fields can be represented globally as exact one-forms, thereby excluding the effects of field traversal and curvature. In this work, we show that this restriction can be relaxed by incorporating nonlocal gauge phase corrections that arise when quantum paths pass through regions of nonzero field strength. These corrections encode a geometric memory of traversal, which persists even in field-free regions. We demonstrate that, within this extended framework, null Lagrangians can be understood as encoding full physical information when supplemented by nonlocal flux memory. As a concrete application, we analyze scalar field propagation near a Schwarzschild horizon and show that the resulting memory effects lead to a frequency-dependent deviation from thermality in Hawking radiation.