Frozen states of charged boson stars

In this paper, we study frozen states of charged boson stars. These solutions are globally regular and exist in a U(1) gauged scalar field model minimally coupled to gravity for suitable choices of the coupling constants. These configurations are field theoretical realizations of the Mazur-Mottola solution with a de Sitter interior, a black hole exterior and a thin shell that interpolates between the two and replaces the event horizon. We demonstrate that standard electrodynamics is sufficient to find these frozen states, but that the self-interaction of the scalar field is crucial. For a sixth-order self-interaction of the scalar field, solutions exist that possess <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>k</a:mi> <a:mo>=</a:mo> <a:mn>2</a:mn> <a:mi>n</a:mi> </a:math> , <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>n</c:mi> <c:mo>∈</c:mo> <c:mi mathvariant="double-struck">N</c:mi> </c:math> nodes in the scalar field. The interval in which these nodes exist corresponds to an additional intermediate shell that corresponds to vacuum. Adding Horndeski vector-tensor gravity to the model allows the frozen states to exist without self-interaction though. The frozen states possess one stable and one unstable lightring, the former inside the thin shell, the latter in the black hole exterior.