Regularization of Gauss-Bonnet Gravity in Riemann-Cartan Geometry

Abstract

We extend the conformal dimensional-derivative regularization of four-dimensional Gauss- Bonnet gravity to Riemann-Cartan geometry, obtaining a regularized action whose torsionless limit equals the well-known regularized four-dimensional Einstein-Gauss-Bonnet model. Varying independently with respect to the scalar, tetrad, and spin connection yields field equations that remain strictly second order in covariant derivatives, thereby avoiding Ostrogradsky-type instabil- ities. Within this framework we obtain static, spherically symmetric black holes carrying torsion hair, showing that the regularized Gauss-Bonnet interaction can support long-range torsion hair without invoking extra dimensions.