Lovelock black holes with a power-Yang-Mills source

TL;DR

This paper explores how raising the Yang-Mills invariant to a power q affects black hole solutions within Einstein-Yang-Mills, Gauss-Bonnet, and Lovelock theories, revealing modifications and potential invariance properties.

Contribution

It introduces a generalized power q for the Yang-Mills invariant and investigates its impact on black hole solutions across various gravity theories.

Findings

Modified black hole solutions depend on the power q.

Conformal invariance emerges in specific dimensions for the power-Yang-Mills source.

Potential for testing the effects of the power q in flat spacetime YM theories.

Abstract

We consider the standard Yang-Mills (YM) invariant raised to the power q, i.e., $(F_{\mu \nu}^{(a)}F^{(a) \mu \nu})^{q}$ as the source of our geometry and investigate the possible black hole solutions. How does this parameter q modify the black holes in Einstein-Yang-Mills (EYM) and its extensions such as Gauss-Bonnet (GB) and the third order Lovelock theories? The advantage of such a power q (or a set of superposed members of the YM hierarchies) if any, may be tested even in a free YM theory in flat spacetime. Our choice of the YM field is purely magnetic in any higher dimensions so that duality makes no sense. In analogy with the Einstein-power-Maxwell theory, the conformal invariance provides further reduction, albeit in a spacetime for dimensions of multiples of 4.