On boundary conditions for linearised Einstein's equations

TL;DR

This paper explores a broad class of boundary conditions for linearised Einstein equations, analyzing their mathematical properties and implications for quantising gravitational waves in curved spacetimes.

Contribution

It introduces and studies generalized boundary conditions for linearised Einstein equations, extending previous proposals and examining their ellipticity, gauge invariance, and spectral properties.

Findings

Boundary conditions are shown to be elliptic and gauge-invariant.

Existence of a spectral gap is established for certain boundary conditions.

Results inform the quantisation of gravitational waves in curved backgrounds.

Abstract

We investigate the properties of a fairly large class of boundary conditions for the linearised Einstein equations in the Riemannian setting, ones which generalise the linearised counterpart of boundary conditions proposed by Anderson. Through the prism of the quest to quantise gravitational waves in curved spacetimes, we study their properties from the point of view of ellipticity, gauge invariance, and the existence of a spectral gap.