# Axial Dissipative Dust as a Source of Gravitational Radiation in f(R) Gravity

## TL;DR

This paper investigates gravitational radiation sources in $f(R)$ gravity by analyzing axially symmetric dissipative dust, finding that spinning configurations emit gravitational waves while non-spinning ones do not.

## Contribution

It introduces a detailed analysis of gravitational radiation in $f(R)$ gravity for axially symmetric dissipative dust, highlighting the role of spin in radiation emission.

## Key findings

- Spinning dust configurations emit gravitational radiation.
- Non-spinning dust configurations do not emit gravitational radiation.
- The super-Poynting vector indicates radiation presence only in spinning cases.

## Abstract

In this paper, we explore the source of gravitational radiation in the context of $f(R)$ gravity by considering axially symmetric dissipative dust under geodesic condition. We evaluate scalars associated with electric and magnetic parts of the Weyl tensor for both non-spinning (at the center) and spinning (in the surrounding of the center) fluids of the configuration. For this purpose, we use the evolution as well as constraint equations for kinematical quantities and Weyl tensor. Finally, we investigate the existence of gravitational radiation through super-Poynting vector. It is found that the fluid is not gravitationally radiating in the non-spinning case but it is gravitationally radiating for the spinning case.