Quasitopological gravity and double-copy formalism

We propose a new approach to the quasitopological theory of gravity based on a modified classical double–copy construction. Focusing on static, spherically symmetric configurations, we show that all vacuum solutions of $D$–dimensional quasitopological gravity can be obtained from an auxiliary non–linear electrodynamics defined in a flat $(D+1)$–dimensional spacetime. The gravitational field equations reduce to an algebraic relation between a primary curvature invariant and the electric field strength, while the remaining dynamics is governed by a Gauss–law constraint for a point–like charge in the auxiliary space. This correspondence provides a transparent interpretation of higher–curvature gravitational interactions in terms of non–linear gauge dynamics and explains the absence of higher–derivative terms in the reduced equations. As illustrative examples, we apply the formalism to Born–Infeld and Hayward–type models, obtaining higher–dimensional regular black–hole solutions with a de~Sitter–like core. Our results extend the scope of the double–copy paradigm beyond Einstein gravity and suggest a unifying framework for a broad class of higher–curvature theories.