Spherical inhomogeneous solutions of Einstein and scalar-tensor gravity: a map of the land

TL;DR

This paper reviews a wide range of spherical and inhomogeneous solutions in Einstein and scalar-tensor gravity theories, highlighting recent developments and relationships among various solutions, with an emphasis on scalar field spacetimes.

Contribution

It provides a comprehensive overview of analytic solutions in scalar-tensor and Einstein gravity, including recent classes like Horndeski and DHOST, emphasizing their interrelations and general geometries.

Findings

Catalogs static and dynamic solutions across multiple theories

Highlights relations and classifications of solutions

Focuses on scalar field geometries and general classes

Abstract

We review spherical and inhomogeneous analytic solutions of the field equations of Einstein and of scalar-tensor gravity, including Brans-Dicke theory, non-minimally (possibly conformally) coupled scalar fields, Horndeski, and beyond Horndeski/DHOST gravity. The zoo includes both static and dynamic solutions, asymptotically flat, and asymptotically Friedmann-Lema\^itre-Robertson-Walker ones. We minimize overlap with existing books and reviews and we place emphasis on scalar field spacetimes and on geometries that are "general" within certain classes. Relations between various solutions, which have largely emerged during the last decade, are pointed out.