The algebraic structure of a cosmological term in spherically symmetric solutions

TL;DR

This paper introduces an algebraic framework for modeling a spherically symmetric cosmological term using an r-dependent tensor, grounded in Petrov classification and Einstein equations, with implications for inflationary cosmology.

Contribution

It presents a novel tensor-based approach to describe the dynamics of a cosmological term in spherically symmetric spacetimes, extending previous models.

Findings

Radial pressure satisfies inflationary equation of state p=-ρ

Tangential pressure derived from conservation equations

Tensor invariant under radial boosts used to characterize the cosmological term

Abstract

We propose to describe the dynamics of a cosmological term in the spherically symmetric case by an r-dependent second rank symmetric tensor invariant under boosts in the radial direction. This proposal is based on the Petrov classification scheme and Einstein field equations in the spherically symmetric case. The inflationary equation of state p=-\rho is satisfied by the radial pressure. The tangential pressure is calculated from the conservation equation (the contracted Bianchi identity).