A classification of spherically symmetric spacetimes

TL;DR

This paper provides a comprehensive classification of spherically symmetric four-dimensional Lorentzian spacetimes based on their local conformal symmetries, including canonical forms and conformal Lie algebras.

Contribution

It introduces a complete classification scheme using conformal decomposition and Petrov type analysis, detailing canonical metrics and symmetry structures.

Findings

Classification of all locally spherically symmetric spacetimes

Explicit forms of conformal Lie algebras for these spacetimes

Discussion of physically meaningful examples

Abstract

A complete classification of locally spherically symmetric four-dimensional Lorentzian spacetimes is given in terms of their local conformal symmetries. The general solution is given in terms of canonical metric types and the associated conformal Lie algebras. The analysis is based upon the local conformal decomposition into 2+2 reducible spacetimes and the Petrov type. A variety of physically meaningful example spacetimes are discussed.