For the p=1/2 Einstein-Maxwell power-Yang-Mills black hole, increasing the hair parameter Q_YM shrinks the horizon, photon sphere, ISCO, shadow, and photon ring, an effect equivalent to a mass shift in Reissner-Nordström.
Lovelock black holes with a power-Yang-Mills source
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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.
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Testing Einstein Maxwell Power-Yang-Mills Hair via Black Hole Photon Rings
For the p=1/2 Einstein-Maxwell power-Yang-Mills black hole, increasing the hair parameter Q_YM shrinks the horizon, photon sphere, ISCO, shadow, and photon ring, an effect equivalent to a mass shift in Reissner-Nordström.