2021/01/31 by Roberto Niardi, Giampiero Esposito, Niardi, Roberto +3
Physics and Astronomy · #Cosmology and Gravitation Theories #Relativity and Gravitational Theory #Black Holes and Theoretical Physics
paper · pdf · doi:10.48550/arxiv.2102.00478
In this paper the Feynman Green function for Maxwell's theory in curved\nspace-time is studied by using the Fock-Schwinger-DeWitt asymptotic expansion;\nthe point-splitting method is then applied, since it is a valuable tool for\nregularizing divergent observables. Among these, the stress-energy tensor is\nexpressed in terms of second covariant derivatives of the Hadamard Green\nfunction, which is also closely linked to the effective action; therefore one\nobtains a series expansion for the stress-energy tensor. Its divergent part can\nbe isolated, and a concise formula is here obtained: by dimensional analysis\nand combinatorics, there are two kinds of terms: quadratic in curvature tensors\n(Riemann, Ricci tensors and scalar curvature) and linear in their second\ncovariant derivatives. This formula holds for every space-time metric; it is\nmade even more explicit in the physically relevant particular cases of\nRicci-flat and maximally symmetric spaces, and fully evaluated for some\nexamples of physical interest: Kerr and Schwarzschild metrics and de Sitter\nspace-time.\n