Regular Bardeen-like black holes in higher-dimensional pure Lovelock gravity with nonlinear Yang–Mills fields

Introduction We construct spherically symmetric, static, and regular Bardeen-like black hole solutions in the framework of higher-dimensional pure Lovelock gravity coupled to nonlinear Yang–Mills (YM) fields. The aim is to generalize the notion of regular black holes to higher-curvature gravity theories while preserving regularity and asymptotic flatness. Methods The gauge fields are modeled using a higher-dimensional Wu–Yang ansatz, and the nonlinear YM Lagrangian is designed to reproduce Bardeen-type configurations known from Einstein gravity. The field equations are solved analytically to obtain exact metric functions, and curvature invariants are computed to verify the regularity of the spacetime. Results The resulting solutions are asymptotically flat and regular at the origin, with all curvature invariants remaining finite throughout the spacetime. In dimensions <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"><mml:mrow><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mi>p</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> , the configurations describe particle-like solutions without horizons. For <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m2"><mml:mrow><mml:mi>N</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>2</mml:mn><mml:mi>p</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> , depending on the model parameters, the solutions can represent either regular black holes or particle-like spacetimes. Analytic conditions determining the existence and number of horizons are derived, allowing for a full classification of the spacetime structure. Discussion A detailed thermodynamic analysis is performed by computing the Hawking temperature and heat capacity. The phase structure reveals regions of thermal stability and the occurrence of first- and second-order phase transitions. These findings extend the concept of regular black holes to pure Lovelock gravity and emphasize the rich interplay between nonlinearity, dimensionality, and gauge dynamics.