Thermal photon fluctuations in a curved spacetime generate metric variance that, in the Fewster-Verch measurement scheme, equals the stochastic gravity noise kernel exactly.
The linearized Einstein equations with sources
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abstract
On vacuum spacetimes of general dimension, we study the linearized Einstein vacuum equations with a spatially compactly supported and (necessarily) divergence-free source. We prove that the vanishing of appropriate charges of the source, defined in terms of Killing vector fields on the spacetime, is necessary and sufficient for solvability within the class of spatially compactly supported metric perturbations. The proof combines classical results by Moncrief with the solvability theory of the linearized constraint equations with control on supports developed by Corvino and Chru\'sciel-Delay.
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Measurements in stochastic gravity and thermal variance
Thermal photon fluctuations in a curved spacetime generate metric variance that, in the Fewster-Verch measurement scheme, equals the stochastic gravity noise kernel exactly.