Conditions for equivalence of static spherically symmetric spacetimes to almost Friedman-Robertson-Walker

TL;DR

This paper identifies the specific conditions under which static spherically symmetric spacetimes can be mathematically equivalent to perturbed Friedman-Robertson-Walker metrics, bridging two important classes of solutions in cosmology and gravitational physics.

Contribution

It provides a detailed set of criteria and a constructive method to establish when these two types of metrics are equivalent, enhancing understanding of their relationship.

Findings

Derived explicit conditions for metric equivalence.

Constructed a correspondence between static and perturbed FRW metrics.

Presented a simple application demonstrating the criteria.

Abstract

We determine the conditions under which a static spherically symmetric spacetime metric is equivalent to a perturbed Friedman-Robertson-Walker metric. We construct the correspondence between the two metrics and discuss a simple application.