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., (Fμν(a)F(a)μν)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.