Torsion singularity in Weitzenböck spacetime (Q1898429)

The authors study spherically symmetric static solutions of an alternative theory of gravity due to \textit{K. Hayashi} and \textit{T. Nakano} [Prog. Theor. Phys. 38, 491 (1967)]. They claim that this theory has vanishing curvature and non-vanishing torsion tensor \(T^\lambda_{\mu \nu}\). However, later in the paper they seem to obtain a non-vanishing Riemann tensor and actually state ``curvature defined by the Christoffel symbols still exists''. They show that for spherically symmetric, static solutions the invariant \(T^\lambda_{\mu \nu} T^{\mu \nu}_\lambda\) diverges at the centre of symmetry.