# Curvature properties of a special type of pure radiation metrics

## TL;DR

This paper investigates the curvature properties of a special class of pure radiation metrics, revealing their semisymmetry, Ricci simplicity, recurrence of curvature forms, and conditions for representing pp-waves, pure radiation, or perfect fluids.

## Contribution

It provides a detailed analysis of the geometric and curvature properties of Ludwig and Edgar's pure radiation metrics, including new conditions for specific physical interpretations.

## Key findings

- The spacetime is semisymmetric and Ricci simple.
- Ricci tensor is Riemann compatible and curvature forms are recurrent.
- The metric can represent generalized pp-waves, pure radiation, or perfect fluids.

## Abstract

A spacetime denotes a pure radiation field if its energy momentum tensor represents a situation in which all the energy is transported in one direction with the speed of light. In 1989, Wils and later in 1997 Ludwig and Edgar studied the physical properties of pure radiation metrics, which are conformally related to a vacuum spacetime. In the present paper we investigate the curvature properties of special type of pure radiation metrics presented by Ludwig and Edgar. It is shown that such a pure radiation spacetime is semisymmetric, Ricci simple, $R$-space by Venzi and its Ricci tensor is Riemann compatible. It is also proved that its conformal curvature 2-forms and Ricci 1-forms are recurrent. We also present a pure radiation type metric and evaluate its curvature properties along with the form of its energy momentum tensor. It is interesting to note that such pure radiation type metric is $Ein(3)$ and 3-quasi-Einstein. We also find out the sufficient conditions for which this metric represents a generalized pp-wave, pure radiation and perfect fluid. Finally we made a comparison between the curvature properties of Ludwig and Edgar's pure radiation metric and pp-wave metrics.