Stability in Cubic Metric-Affine Gravity

TL;DR

This paper investigates the stability of vector and axial modes in cubic Metric-Affine Gravity, showing that cubic invariants can cancel instabilities and yield black hole solutions with dynamical torsion and nonmetricity.

Contribution

It demonstrates how cubic order invariants stabilize vector and axial modes and provides new black hole solutions with massive torsion and nonmetricity.

Findings

Cubic invariants cancel instabilities in vector and axial sectors.

Black hole solutions with dynamical torsion and nonmetricity are found.

Massive tensor modes avoid no-go theorems for higher spin interactions.

Abstract

We analyse the stability issue of the vector and axial modes of the torsion and nonmetricity tensors around general backgrounds in the framework of cubic Metric-Affine Gravity. We show that the presence of cubic order invariants defined from the curvature, torsion and nonmetricity tensors allow the cancellation of the well-known instabilities arising in the vector and axial sectors of quadratic Metric-Affine Gravity. For the resulting theory, we also obtain Reissner-Nordstr\"om-like black hole solutions with dynamical torsion and nonmetricity, which in general include massive tensor modes for these quantities, thus avoiding further no-go theorems that potentially prevent a consistent interaction of massless higher spin fields in the quantum regime.