# 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.

## Key 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.