# Labeling spherically symmetric spacetimes with the Ricci tensor

## TL;DR

This paper completes the intrinsic classification of spherically symmetric spacetimes by analyzing Ricci tensor types, providing explicit labels for key solutions like Schwarzschild interior and Vaidya, and characterizing Stephani universes.

## Contribution

It introduces a comprehensive intrinsic labeling method for spherically symmetric solutions based on Ricci tensor algebraic types, extending previous work.

## Key findings

- Explicit labeling of Schwarzschild interior and Vaidya solutions.
- Characterization of conformally flat perfect fluid and Einstein-Maxwell solutions.
- Intrinsic classification of Stephani universes.

## Abstract

We complete the intrinsic characterization of spherically symmetric solutions partially accomplished in a previous paper [Class.Quant.Grav. (2010) 27 205024]. In this approach we consider every compatible algebraic type of the Ricci tensor, and we analyze specifically the conformally flat case for perfect fluid and Einstein-Maxwell solutions. As a direct application we obtain the {\em ideal} labeling (exclusively involving explicit concomitants of the metric tensor) of the Schwarzschild interior metric and the Vaidya solution. The Stephani universes and some significative subfamilies are also characterized.