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 $\left(-4{\beta }_4{+k}_1{\beta }_5{/2k}_0{+k}_2{\gamma }_4{/k}_0\right)/\kappa z_4\ne 0$ on the coupling constants. For the special case $\left(-4{\beta }_4{+k}_1{\beta }_5{/2k}_0{+k}_2{\gamma }_4{/k}_0\right)/\kappa z_4=0,$ it follows that the only static non-extremal black hole is the Reissner-Nordström one. The results can be extended to exclude also the existence of soliton solutions of the triplet sector of MAG.