Authors derive the second term in the wave-trace expansion on stationary spacetimes as an analogue of the second heat kernel coefficient, reducing to the scalar curvature term for ultrastatic metrics.
B\"ar, A.Strohmaier, Local Index Theory for Lorentzian Manifolds, arXiv: 2012.01364
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Hadamard coefficients for normally hyperbolic operators are recoverable from Green's operators via added resolvent data, powers, or manifold products.
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Heat and Wave kernel expansions for stationary spacetimes
Authors derive the second term in the wave-trace expansion on stationary spacetimes as an analogue of the second heat kernel coefficient, reducing to the scalar curvature term for ultrastatic metrics.
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Formulas for Hadamard coefficients in terms of Green's operators
Hadamard coefficients for normally hyperbolic operators are recoverable from Green's operators via added resolvent data, powers, or manifold products.