We prove that, up to multiplication by a scalar, the Minkowski metric tensor is the only second-order tensor that is Lorentz-invariant. To prove this, we show that a specific set of three $4\times 4$ matrices, made of two rotation matrices plus a Lorentz boost, is irreducible.
Mayeul Arminjon. "Lorentz-Invariant Second-Order Tensors and an Irreducible Set of Matrices." J. Geom. Symmetry Phys. 50 1 - 10, 2018. https://doi.org/10.7546/jgsp-50-2018-1-10