Anisotropic matter and nonlinear electromagnetics black holes

It is shown that anisotropic matter black holes with two parameters w and K correspond to nonlinear electrodynamics (NED) black holes with power-index s and charge term ξ (s,q) ξ ( s , q ) by introducing a NED term. These NED black holes include dark matter ( $$s=3/4$$ s = 3 / 4 ), constant scalar hair ( $$s=1$$ s = 1 ), charged quantum Oppenheimer–Snyder ( $$s=3/2$$ s = 3 / 2 ), and Einstein–Euler–Heisenberg ( $$s=2$$ s = 2 ) black holes derived from their known actions. Rotating NED black holes can be obtained from rotating anisotropic matter black holes when replacing w and K by $$2s-1$$ 2 s - 1 and ξ (s,q) ξ ( s , q ) . The extremal rotating NED black holes being the boundary between rotating charged NED black hole and naked singularity are derived as functions of the rotation parameter a ( q ).