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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.