Uniqueness theorems for static black holes in metric-affine gravity

TL;DR

This paper proves that in a specific sector of metric-affine gravity, the only static black holes are Schwarzschild or Reissner-Nordström, depending on the coupling constants, and rules out soliton solutions.

Contribution

It establishes uniqueness theorems for static black holes in the triplet sector of metric-affine gravity, extending previous results and excluding soliton solutions.

Findings

Schwarzschild is the only static black hole under certain conditions

Reissner-Nordström is the only static non-extremal black hole in a special case

Soliton solutions are excluded in the triplet sector of MAG

Abstract

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 (-4\beta_4 + k_1\beta_5/2k_0 + k_2\gamma_4/k_0)/\kappa z_4 \neq 0 on the coupling constants. For the special case (-4\beta_4 + k_1\beta_5/2k_0 + k_2\gamma_4/k_0)/\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.