Slow-rotating dirty black hole in Einstein-nonlinear electrodynamics-dilaton theory

In this study, we aim to obtain a slow-rotating black hole in the theory of gravity coupled to square- root nonlinear electrodynamics and a dilaton scalar field. Its static and spherically symmetric version has been recently found in EPJC83(2023)406 which is a 2-parameter non-asymptotically flat black hole with a singularity located at its center. In its slow-rotating version, the solution is a three-parameter black hole that is also non-asymptotically flat and singular at its center. The electric field up to the first order of the rotation parameter is uniform in analogy with its static counterpart.