Spectral Behavior of the Linearized Einstein Operator and the Infrared Structure of Linearized Gravity
ORAL
Abstract
This work analyzes the spectral structure of the linearized Einstein operator in harmonic gauge on asymptotically flat three-manifolds, regarded as the one-particle Hamiltonian for quantized linearized gravity. When the background curvature decays faster than the inverse cube of the radius, the curvature potential is a relatively compact perturbation, and the essential spectrum remains [0,∞), corresponding to a radiative graviton sector. At the critical inverse-cube decay, compactness fails, and zero becomes embedded in the essential spectrum through a normalized Weyl sequence satisfying the linearized constraints. This identifies the sharp geometric threshold at which the spatial graviton spectrum develops a continuum of arbitrarily soft modes; the static, linearized counterpart of the infrared sector associated with gravitational memory and soft-graviton theorems. The result provides a geometric criterion for the onset of infrared sensitivity in asymptotically flat spacetimes and clarifies the spatial origin of soft sectors in quantum gravity.
*No funding was received or used.
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Publication: This presentation builds on my preprint 'Curvature Decay and Spectrum of the Nonabelian Laplacian on R³', which develops the spectral threshold framework for gauge-field Laplacians. That preprint was presented as an oral contributed talk at the joint TAOAPS conference on Oct. 11. An earlier version of that research was also peer reviewed in Annales Henri Poincaré. The present work extends that analysis to the linearized Einstein operator on asymptotically flat manifolds. A preprint write-up is planned for this extension.
Presenters
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Michael Wilson
- University of Arkansas at Little Rock