Regularization of Gauss-Bonnet gravity in Riemann-Cartan geometry
Phys. Rev. D 113, 064045 – Published 24 March, 2026
DOI: https://doi.org/10.1103/sqty-rn64
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 instabilities. 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.
