On the Significance of the Weyl Curvature in a Relativistic Cosmological Model

TL;DR

This paper emphasizes the importance of Weyl curvature in relativistic cosmology, showing that both Newtonian and anti-Newtonian fields are essential for accurate gravitational modeling and wave solutions.

Contribution

It introduces a set of constraints and propagation equations for Weyl fields, highlighting the necessity of both fields for realistic relativistic models.

Findings

Purely Newtonian models are inconsistent with relativity.

Both Weyl fields are required for nonlocal and radiative gravitational solutions.

Explicit solutions for gravitational waves are derived.

Abstract

The Weyl curvature includes the Newtonian field and an additional field, the so-called anti-Newtonian. In this paper, we use the Bianchi and Ricci identities to provide a set of constraints and propagations for the Weyl fields. The temporal evolutions of propagations manifest explicit solutions of gravitational waves. We see that models with purely Newtonian field are inconsistent with relativistic models and obstruct sounding solutions. Therefore, both fields are necessary for the nonlocal nature and radiative solutions of gravitation.