Quasitopological gravity and double-copy formalism

TL;DR

This paper introduces a novel approach to quasitopological gravity using a modified double-copy method, linking higher-curvature solutions to non-linear electrodynamics in higher dimensions, and providing new regular black hole solutions.

Contribution

It develops a new double-copy framework for quasitopological gravity, connecting vacuum solutions to auxiliary non-linear electrodynamics, and extends the double-copy paradigm beyond Einstein gravity.

Findings

All vacuum solutions derived from an algebraic relation in the new formalism.

Higher-dimensional regular black holes with de Sitter cores obtained.

The approach clarifies the role of gauge dynamics in higher-curvature gravity.

Abstract

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.