Conformally Flat Collapsing Stars in f (R) gravity

TL;DR

This paper analytically investigates the collapse of a spherical star in f(R) gravity, examining the interior conformal flatness, matching conditions, and physical quantities to understand the collapse dynamics and singularity formation.

Contribution

It provides an analytical model of star collapse in f(R) gravity with conformal flatness and studies the effects of inhomogeneity and heat flux on collapse outcomes.

Findings

Collapse rate diminishes due to heat conduction and inhomogeneity.

Singularity forms asymptotically with zero proper volume.

Physical quantities like density and pressure are spatially distributed.

Abstract

The present work includes an analytical investigation of a collapsing spherical star in f (R) gravity. The interior of the collapsing star admits a conformal flatness. Information regarding the fate of the collapse is extracted from the matching conditions of the extrinsic curvature and the Ricci curvature scalar across the boundary hypersurface of the star. The radial distribution of the physical quantities such as density, anisotropic pressure and radial heat flux are studied. The inhomogeneity of the collapsing interior leads to a non-zero acceleration. The divergence of this acceleration and the loss of energy through a heat conduction forces the rate of the collapse to die down and the formation of a zero proper volume singularity is realized only asymptotically.