Exact Nonnull Wavelike Solutions to Gravity with Quadratic Lagrangians

TL;DR

This paper derives exact nonnull wave-like solutions in quadratic Lagrangian gravity theories, revealing new insights into gravitational radiation and energy transfer beyond linear approximations.

Contribution

It provides explicit solutions with specific metric components and Riemann tensor forms, expanding understanding of gravitational waves in quadratic gravity models.

Findings

Solutions depend on Riemann tensor cross terms

Supports existence of nonnull gravitational radiation

Constructs gravitational energy Poynting vectors

Abstract

Solutions to gravity with quadratic Lagrangians are found for the simple case where the only nonconstant metric component is the lapse $N$ and the Riemann tensor takes the form $R^{t}_{.itj}=-k_{i}k_{j}, i,j=1,2,3$; thus these solutions depend on cross terms in the Riemann tensor and therefore complement the linearized theory where it is the derivatives of the Riemann tensor that matter. The relationship of this metric to the null gravitational radiation metric of Peres is given. Gravitaional energy Poynting vectors are construcetd for the solutions and one of these, based on the Lanczos tensor, supports the indication in the linearized theory that nonnull gravitational radiation can occur.