Wyman's "other" scalar field solution, Sultana's generalization, and their Brans-Dicke and $R^2$ relatives

Abstract

Wyman's less known static and spherically symmetric solution of the Einstein-Klein-Gordon equations and its recent generalization for positive cosmological constant are discussed, showing that they contain central naked singularities. By mapping back to the Jordan frame, we obtain the conformal cousins of these geometries that solve the vacuum Brans-Dicke field equations and are time-dependent and spherical. Their physical nature is discussed and the geometry is shown to be also a solution of purely quadratic gravity.

Explanation and references added, matches version accepted in Phys. Rev. D

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Cited by in corpus (10)

• Hairy black holes in DHOST theories: Exploring disformal transformation as a solution-generating method
• Spherical inhomogeneous solutions of Einstein and scalar-tensor gravity: a map of the land
• Searching for dynamical black holes in various theories of gravity
• Integrable modified gravity cosmological models with an additional scalar field
• Disformal mappings of spherical DHOST geometries
• Conformal and kinetic couplings as two Jordan frames of the same theory
• Stationary spacetimes with time-dependent real scalar fields
• The curious case of the Buchdahl-Land-Sultana-Wyman-Ibañez-Sanz spacetime
• Brans-Dicke analogue of the Roberts geometry
• A new approach to the thermodynamics of scalar-tensor gravity