Magnetic black hole in Einstein-Dilaton-Square root nonlinear electrodynamics

Starting from the most general action in Einstein-Dilaton-Nonlinear Electrodynamics (NED) theory, we obtain field equations. We apply equations for specific NED known as square root model coupled nonminimally to dilaton scalar whose self-interaction is Liouville type plus a cosmological constant and solve With pure magnetic it shown that strong limit of Born–Infeld theory. In static spherically symmetric spacetime monopole sitting at origin, are exactly solvable provided integration constants solutions theory appearing linked through two constraints. As known, such an exact solution absence i.e., gravity doesn’t exist. Therefore, presence gives additional freedom The obtained singular non-asymptotically flat depending on free parameters may be black hole or object. For spacetime, study thermal stability show thermally stable its size larger than critical value.