Logarithmic correction to the entropy of extremal black holes in $$ \mathcal{N} $$ = 1 Einstein-Maxwell supergravity

A bstract We study one-loop covariant effective action of “non-minimally coupled” $$ \mathcal{N} N = 1, d 4 Einstein-Maxwell supergravity theory by heat kernel tool. By fluctuating the fields around classical background, we functional determinant Laplacian differential operator following Seeley-DeWitt technique expansion in proper time. then compute coefficients obtained through expansion. particular coefficient is used for determining logarithmic correction to Bekenstein-Hawking entropy extremal black holes using quantum function formalism. thus determine Kerr-Newman, Kerr and Reissner-Nordström theory.