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

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-Lemaître-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.

arXiv comment140 pages, one figure. Explanation text and bibliography expanded, typographical errors corrected. Matches version to appear in Physics Reports

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• Novel exact ultra-compact and ultra-sparse hairy black holes emanating from regular and phantom scalar fields
• Past-directed scalar field gradients and scalar-tensor thermodynamics
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• The covariant approach to static spacetimes in Einstein and extended gravity theories
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• Tolman-Ehrenfest's criterion of thermal equilibrium extended to conformally static spacetimes
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