Globally regular charged black holes in non-polynomial quasi-topological gravity with Born-Infeld electrodynamics

We construct exact static, spherically symmetric charged solutions in four-dimensional non-polynomial quasi-topological gravity coupled to Born-Infeld electrodynamics. We focus on the model $h(p)=p\mathrm{/}(1+{\mathrm{\ell }}^{2}p)$, whose vacuum branch develops a curvature singularity at a finite radius. We show that Born-Infeld nonlinearities can remove this singularity within a finite region of parameter space, yielding globally regular geometries with an asymptotically flat exterior and a finite-curvature AdS-type core. The regular sector contains both horizonless configurations and RBHs, separated by a degenerate-horizon boundary. We further identify a continuous branch of regular black holes with a triple-degenerate inner horizon and a simple outer event horizon, satisfying ${\kappa }_{-}=0$ and ${\kappa }_{+}\mathrm{\ne }0$. This provides a converse example to cases in which introducing charge spoils the regularity of a vacuum regular black hole. In the present model, Born-Infeld electrodynamics instead removes the finite-radius singularity of a vacuum-singular gravitational branch while supporting globally regular charged geometries, including RBHs with nontrivial inner-horizon structure.