Lovelock black holes with a power-Yang–Mills source

Abstract

We consider the standard Yang–Mills (YM) invariant raised to the power q , i.e., View the MathML source 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.