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In this note, we consider perturbations of Minkowski space as well as moregeneral spacetimes on which the wave operator $\square_g$ is essentiallyself-adjoint. We review a recent result which gives the meromorphiccontinuation of the Lorentzian spectral zeta function density, i.e. of thetrace density of complex powers $\alpha \mapsto (\square_g-i\varepsilon)^{-\alpha}$. In even dimension $n\geq 4$, the residue at$\frac{n}{2}-1$ is shown to be a multiple of the scalar curvature in the limit$\varepsilon\to 0^+$. This yields a spectral action for gravity in Lorentziansignature.

Lorentzian spectral zeta functions on asymptotically Minkowski spacetimes