The Horizon Trident: A No-Go Theorem for Quantum Fields on Spherically-Symmetric, Continuous Spacetimes with Non-Extremal Horizons Alexander Yiannopoulos * Chökhor Düchen, 2025 We establish a fundamental mathematical incoherence that arises from the application of quantum field theory to a spacetime containing a classical, continuous, non-rotating, non-extremal event horizon. By rigorously analyz- ing the foundational case of a massless scalar field, we demonstrate that no choice of quantum vacuum state provides a physically consistent description of spherically symmetric gravitational collapse. Any plausible state for a col- lapsing star necessarily violates at least one of three foundational principles: (i) the physically-motivated in-vacuum violates the Equivalence Principle via a non-renormalizable divergence at the horizon; (ii) any state constructed to be regular on the horizon requires a past history of negative energy flux that violates rigorously established Quantum Energy Inequalities (QEIs); and (iii) any well-behaved Hadamard state, including the Unruh vacuum, exhibits a universal pathology of divergent vacuum energy fluctuations, indicating a fatal breakdown of the semiclassical approximation precisely at the horizon. The axioms of local quantum field theory and general relativity (in the form of a smooth manifold) are therefore mutually inconsistent for any non-rotating, non-extremal causal horizon, as we argue the geometric and quantum principles that lead to this trilemma are not unique to scalar fields but are generic features of horizons. * Email: ayiannopoulos@protonmail.com 1