Generalized Einstein-Maxwell theory: Seeley-DeWitt coefficients and logarithmic corrections to the entropy of extremal and nonextremal black holes

We present a consolidated manual of Euclidean gravity approaches for finding the logarithmic corrections to entropy full Kerr-Newman family black holes in both extremal and non-extremal limits. Seeley-DeWitt coefficients quadratic fluctuations concern theory appear be key ingredients this manual. Following manual, we calculate first three generalized Einstein-Maxwell minimally-coupled additional massless scalar, vector, spin-1/2 Dirac spin-3/2 Rarita-Schwinger fields. finally employ data reproduce all $\mathcal{N} \geq 2$ supergravity via an alternative local supersymmetrization method.