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Compact boson stars in \(K\) field theories. (English) Zbl 1203.83020

Summary: We study a scalar field theory with a non-standard kinetic term minimally coupled to gravity. We establish the existence of compact boson stars, that is, static solutions with compact support of the full system with self-gravitation taken into account. Concretely, there exist two types of solutions, namely compact balls on the one hand, and compact shells on the other hand. The compact balls have a naked singularity at the center. The inner boundary of the compact shells is singular, as well, but it is, at the same time, a Killing horizon. These singular, compact shells therefore resemble black holes.

MSC:

83C57 Black holes
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
83C15 Exact solutions to problems in general relativity and gravitational theory
85A15 Galactic and stellar structure
81T20 Quantum field theory on curved space or space-time backgrounds
83C75 Space-time singularities, cosmic censorship, etc.
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