The wave resolvent for compactly supported perturbations of static spacetimes

2022/04/19 by Wrochna, Michał, Zeitoun, Ruben
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2204.08767

Abstract

In this note, we consider the wave operator \square_g in the case of globally hyperbolic, compactly supported perturbations of static spacetimes. We give an elementary proof of the essential self-adjointness of \square_g and of uniform microlocal estimates for the resolvent in this setting. This provides a model for studying Lorentzian spectral zeta functions which is particularly simple, yet sufficiently general for locally deriving Einstein equations from a spectral Lagrangian.

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