Spherical doubly warped spacetimes for radiating stars and cosmology

TL;DR

This paper explores the geometric and physical properties of doubly warped spherically symmetric spacetimes, deriving conditions for stellar collapse, cosmological models, and extensions to f(R) gravity, highlighting their implications for anisotropic fluids and radiation.

Contribution

It provides a comprehensive analysis of doubly warped spacetimes, including Weyl and Ricci tensors, junction conditions, and extensions to f(R) gravity, advancing understanding of inhomogeneous cosmology and radiating stars.

Findings

Derived the structure of the Weyl and Ricci tensors in DW spacetimes.

Established junction conditions for radiating stellar collapse models.

Extended the framework to include f(R) gravity with anisotropic fluids.

Abstract

Spherically symmetric spacetimes are ambient spaces for models of stellar collapse and inhomogeneous cosmology. We obtain results for the Weyl tensor and the covariant form of the Ricci tensor on general doubly warped (DW) spacetimes. In a spherically symmetric metric, the Ricci and electric tensors become rank-2, built with a velocity vector field and its acceleration. Their structure dictates the general form of the energy-momentum tensor in the Einstein equations in DW spherical metrics. The anisotropic pressure and the heat current of an imperfect fluid descend from the gradient of the acceleration and the electric part of the Weyl tensor. For radiating stellar collapse with heat flow, the junction conditions of the doubly warped metric with the Vaidya metric are reviewed, with the boundary condition for the radial pressure. The conditions for isotropy simply accomodate various models in the literature. The anisotropy of the Ricci tensor in the special case of spherical GRW space-times (geodesic velocity), gives Friedmann equations deviating from standard FRW cosmology by terms due to the electric tensor. We introduce "perfect 2-scalars" to discuss f(R) gravity with anisotropic fluid source in a doubly warped spacetime, and show that the new geometric terms in the field equations do not change the tensor structure of the fluid energy-momentum tensor.