Microlocal Spectral Asymptotics of Non-Self-Adjoint Operators and the Anomalous Propagation of Gevrey Singularities Near Degenerate Event Horizons

Mathematical Applications of Science Fiction We present a rigorous microlocal analysis of the spectral properties of a class of non-self-adjoint semiclassical pseudodifferential operators acting on compact manifolds equipped with a degenerate Lorentzian metric characteristic of event horizons in trans-universal geometries. Specifically, we study the propagation of Gevrey-s singularities, for s greater than one, through the characteristic set of operators containing parity-time symmetry breaking terms. By constructing a global escape function in the complexified phase space and applying a modified Fourier–Bros–Iagolnitzer transform, we derive sharp resolvent estimates in the semiclassical limit. We establish a Weyl-type law governing the eigenvalue distribution in the strongly non-self-adjoint regime, revealing an anomalous accumulation of spectrum along certain Stokes lines emerging from the degenerate horizon. Furthermore, we prove that the wavefront set of the propagator exhibits a bifurcation at the radial points of the horizon, producing a leakage of singularities into the classically forbidden region—a mechanism identified as the mathematical origin of interdimensional instability.