2022/02/13 by Nguyen Viet Dang, Dang, Nguyen Viet, Michał Wrochna +1
Physics and Astronomy · #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.2202.06408
openalex publication_date 2022/02/13 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
In this note, we consider perturbations of Minkowski space as well as more general spacetimes on which the wave operator \squareg is essentially self-adjoint. We review a recent result which gives the meromorphic continuation of the Lorentzian spectral zeta function density, i.e. of the trace density of complex powers α↦ (\squareg-i ε)-α. In even dimension n≥ 4, the residue at (n)/(2)-1 is shown to be a multiple of the scalar curvature in the limit ε→ 0+. This yields a spectral action for gravity in Lorentzian signature.