Plane torsion waves in quadratic gravitational theories

TL;DR

This paper investigates plane torsion waves within quadratic gravitational theories, deriving conditions for their existence and providing mathematical tools for analyzing such solutions in the context of Riemann-Cartan spaces.

Contribution

It introduces the conditions under which torsion plane waves exist in quadratic gravitational theories and develops mathematical formulas for variational analysis using exterior differential forms.

Findings

Existence conditions for torsion plane waves derived

Restrictions on coupling constants identified

Mathematical framework for variational procedures established

Abstract

The definition of the Riemann-Cartan space of the plane wave type is given. The condition under which the torsion plane waves exist is found. It is expressed in the form of the restriction imposed on the coupling constants of the 10-parametric quadratic gravitational Lagrangian. In the mathematical appendix the formula for commutator of the variation operator and Hodge operator is proved. This formula is applied for the variational procedure when the gravitational field equations are obtained in terms of the exterior differential forms.