Ergosphere and shadow of a rotating regular black hole

The spacetime singularities in classical general relativity predicted by the celebrated singularity theorems are formed at the end of gravitational collapse. Quantum gravity is the expected theory to resolve the singularity problem, but we are now far from it. Therefore attention has shifted to models of regular black holes free from the singularities. A spherically symmetric regular toy model was obtained by Dymnikova (1992) which we demonstrate as an exact solution of Einstein's field equations coupled to nonlinear electrodynamics for a Lagrangian with parameter $b$ related to magnetic charge. We construct rotating counterpart of this solution which encompasses the Kerr black hole as a special case when charge is switched off ($b=0$). Event Horizon Telescope has released the first image of supermassive black hole M87$^*$, revealing the structure near black hole horizon. The rotating regular black hole's shadow may be useful to determine strong field regime. We investigate ergosphere and black hole shadow of rotating regular black hole to infer that their sizes are sensitive to charge $b$ and have a richer chaotic structure. In particular, rotating regular black hole possess larger size, but less distorted shadows when compared with Kerr black holes. We find one to one correspondence between ergosphere and shadow of the black hole.