Semiclassical Gravity in Static Spacetimes as a Constrained Initial Value Problem

@article{JuarezAubry2021SemiclassicalGI,
  title={Semiclassical Gravity in Static Spacetimes as a Constrained Initial Value Problem},
  author={Benito A. Ju'arez-Aubry},
  journal={Annales Henri Poincar{\'e}},
  year={2021},
  volume={23},
  pages={1451-1487}
}
We study the semiclassical Einstein field equations with a Klein–Gordon field in ultrastatic and static spacetimes. In both cases, the equations for the spacetime metric become constraint equations. In the ultrastatic case, the Hadamard singular structure can be characterised explicitly, which allows one to in principle give initial data for the Wightman function that has correct distributional singularities, such that the expectation value of the renormalised stress–energy tensor of the… 
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