The r^{-3} curvature decay is a universal threshold that makes zero part of the essential spectrum of the linearized coupled Einstein-Maxwell operator via delocalized modes, unifying the infrared behavior of spin-1, spin-2, and mixed fields and linking it to memory effects.
Elliptic Differential Operators on Noncompact Man- ifolds,
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Infrared Universality: The $r^{-3}$ Spectral Threshold for Coupled Gravitational and Electromagnetic Fields
The r^{-3} curvature decay is a universal threshold that makes zero part of the essential spectrum of the linearized coupled Einstein-Maxwell operator via delocalized modes, unifying the infrared behavior of spin-1, spin-2, and mixed fields and linking it to memory effects.