A comment on metric vs metric-affine gravity


Lındström U. G., Sarıoğlu B. Ö.

PHYSICS LETTERS, SECTION B: NUCLEAR, ELEMENTARY PARTICLE AND HIGH-ENERGY PHYSICS, vol.836, pp.137619, 2023 (SCI-Expanded) identifier

Abstract

We consider the sum of the Einstein-Hilbert action and a Pontryagin density (PD) in arbitrary even dimension ≥ 4. All curvatures are functions of independent affine (torsionless) connections only. In arbitrary even dimension, not only in 4n, these first order PD terms are shown to be covariant divergences of “Chern-Simons” currents. The field equation for the connection leads to it being Levi- Civita, and to the metric and affine field equations being equivalent to the second order metric theory. This result is a counterexample to the theorem stating that purely metric and metric-affine models can only be equivalent for Lovelock theories.