Regularization of Gauss-Bonnet Gravity in Riemann-Cartan Geometry

TL;DR

This paper extends regularization techniques of Gauss-Bonnet gravity to Riemann-Cartan geometry, resulting in second-order field equations and revealing black holes with torsion hair supported by the regularized interaction.

Contribution

It introduces a regularized Gauss-Bonnet action in Riemann-Cartan geometry that maintains second-order equations and supports torsion hair in black holes.

Findings

Regularized action reduces to known Einstein-Gauss-Bonnet model in torsionless limit.

Field equations remain second order, avoiding Ostrogradsky instabilities.

Black holes with torsion hair are supported by the regularized interaction.

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.