Generating Minimally Coupled Einstein-Scalar Field Solutions from Vacuum Solutions with Arbitrary Cosmological Constant

TL;DR

This paper extends solution-generating techniques for Einstein-scalar fields to include arbitrary cosmological constants, resulting in new cosmological models with horizons and scalar black holes, broadening the understanding of scalar field cosmologies.

Contribution

It generalizes the Buchdahl and Fonarev transformations to generate Einstein-scalar solutions from vacuum solutions with any cosmological constant, revealing a new class of solutions.

Findings

Derived a two-parameter family of expanding, accelerating cosmologies.

Identified solutions with cosmological horizons at pi/2 angular distance.

Found solutions describing scalar black hole formation at late times.

Abstract

This paper generalizes two previously known techniques for generating minimally coupled Einstein-scalar field solutions in 4 dimensions; the Buchdahl and Fonarev transformations. By applying this solution generation technique, minimally coupled Einstein-scalar field solutions can be generated from vacuum solutions with arbitrary cosmological constant in arbitrary dimension. The only requirement to a seed solution is that it posesses a hypersurface-orthogonal Killing vector field. The generalization that allows us to use seed solutions with arbitrary cosmological constant uncovers a new class of Einstein-scalar field solutions that has previously not been studied. We apply the new solution transformation to the (A)dS4 vacuum solution. Transforming the resulting Einstein-scalar field solution to the conformal frame, a two-parameter family of spatially finite, expanding and accelerating cosmological solutions are found that are conformally isometric to the Einstein static universe RxS^3. We study null geodesics and find that for any observer, the solution has a cosmological horizon at an angular distance of pi/2 away from the observer. We find that a subset of these solutions can be naturally interpreted as expanding cosmologies in which a scalar black hole is formed at late times. The conformally coupled scalar field satisfies the weak energy condition as long as the energy density is positive, while the strong energy condition is generally violated.