Review of gravitational wave solutions in quadratic metric-affine gravity

Abstract

In this review we consider the quadratic Metric-Affine Gauge gravity Lagrangian, which contains all the algebraic invariants up to quadratic order in torsion, nonmetricity and curvature. The goal will be to collect the known exact solutions for this theory that describe the propagation of a gravitational wave and some useful properties. We concentrate on solutions whose connections are different from the Levi-Civita one and provide also the extension of already known axial torsion solutions to more general Lagrangians. At the end, we will briefly discuss colliding waves and Riemannian solutions.

31 pages, 1 figure, contribution to the Special Issue of the International Journal of Geometric Methods in Modern Physics dedicated to the conference Geometric Foundations of Gravity in Tartu 2021

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Cited by in corpus (6)

• New black hole solutions with a dynamical traceless nonmetricity tensor in Metric-Affine Gravity
• Vector stability in quadratic metric-affine theories
• Spatially covariant gravity with nonmetricity
• Algebraic classification of the gravitational field in Weyl-Cartan space-times
• Algebraic classification of the gravitational field in general metric-affine geometries
• Gravitational waves in Cubic Metric-Affine Gravity