Abstract
We study generalisations of the Schwarzschild-de Sitter solution in the presence of a scalar field with a potential barrier. These static, spherically symmetric solutions have two horizons, in between which the scalar interpolates at least once across the potential barrier, thus developing a lump. In part, we recover solutions discussed earlier in the literature and for those we clarify their properties. But we also find a new class of solutions in which the scalar lump curves the spacetime sufficiently strongly so as to change the nature of the erstwhile cosmological horizon into an additional trapped horizon, resulting in a scalar lump surrounded by two black holes. These new solutions appear in a wide range of the parameter space of the potential. We also discuss (challenges for) the application of all of these solutions to black hole seeded vacuum decay.
Highlights
The no-hair conjecture, formulated as no-hair theorems for concrete matter contents [1], restricts the ways one can attach nontrivial field configuration to a black hole solution
We find a new class of solutions in which the scalar lump curves the spacetime sufficiently strongly so as to change the nature of the erstwhile cosmological horizon into an additional trapped horizon, resulting in a scalar lump surrounded by two black holes
We have investigated solutions of general relativity exhibiting two horizons, in the presence of a scalar field with a potential barrier
Summary
The no-hair conjecture, formulated as no-hair theorems for concrete matter contents [1], restricts the ways one can attach nontrivial field configuration to a black hole solution. One of the ways to overcome the restrictions of the no-hair conjecture is to consider a self-interacting scalar field theory with nontrivial potential, and coupled to gravity. [2] that in the case of a nonmonotonic scalar field potential there are static Schwarzschild-de Sitter (SdS) like solutions with the scalar field oscillating between different sides of a potential barrier. Such solutions with two horizons and an oscillating scalar field were recently rediscovered in Ref. In Ref. [3], only the properties of solutions in between the two horizons were investigated, since this is the only part that is relevant for phase transitions described by Euclidean methods
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