Non-local scalar fields in static spacetimes via heat kernels

@inproceedings{Kolavr2022NonlocalSF,
  title={Non-local scalar fields in static spacetimes via heat kernels},
  author={Ivan Kol'avr},
  year={2022}
}
We solve the non-local equation −e−` 2 φ = J for i) static scalar fields in static spacetimes and ii) time-dependent scalar fields in ultrastatic spacetimes. Corresponding equations are rewritten as non-local Poisson/inhomogeneous Helmholtz equations in compact and non-compact weighted/Riemannian manifolds using static/frequency-domain Green’s functions, which can be computed from the heat kernels in the respective manifolds. With the help of the heat kernel estimates, we derive the static… 

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