Uniqueness theorems for static black holes in metric-affine gravity

Using the equivalence theorem for the triplet ansatz sector of metric-affine gravity (MAG) theories and the Einstein-Proca system, it is shown that the only static black hole of the triplet sector of MAG is the Schwarzschild solution, under the constraint $(\ensuremath{-}4{\ensuremath{\beta}}_{4}{+k}_{1}{\ensuremath{\beta}}_{5}{/2k}_{0}{+k}_{2}{\ensuremath{\gamma}}_{4}{/k}_{0})/\ensuremath{\kappa}{z}_{4}\ensuremath{\ne}0$ on the coupling constants. For the special case $(\ensuremath{-}4{\ensuremath{\beta}}_{4}{+k}_{1}{\ensuremath{\beta}}_{5}{/2k}_{0}{+k}_{2}{\ensuremath{\gamma}}_{4}{/k}_{0})/\ensuremath{\kappa}{z}_{4}=0,$ it follows that the only static non-extremal black hole is the Reissner-Nordstr\"om one. The results can be extended to exclude also the existence of soliton solutions of the triplet sector of MAG.

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