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Gravastar-like black hole solutions in \(q\)-theory. (English) Zbl 1528.83085

Summary: We present a stationary spherically symmetric solution of the Einstein equations, with a source generated by a scalar field of \(q\)-theory. In this theory Riemannian gravity, as described by the Einstein-Hilbert action, is coupled to a three-form field that describes the dynamical vacuum. Formally it behaves like a matter field with its own stress-energy tensor, equivalent to a scalar field minimally coupled to gravity. The asymptotically flat solutions obtained to the field equations represent black holes (BHs). For a sufficiently large horizon radius the energy density is localized within a thin spherical shell situated just outside of the horizon, analogous to a gravastar. The resulting solutions to the field equations, which admit this class of configurations, satisfy existence conditions that stem from the BH no-hair theorem, thanks to the presence of a region in space in which the energy density is negative.

MSC:

83C57 Black holes
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
33C55 Spherical harmonics
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83C30 Asymptotic procedures (radiation, news functions, \(\mathcal{H} \)-spaces, etc.) in general relativity and gravitational theory
14B25 Local structure of morphisms in algebraic geometry: étale, flat, etc.
85A15 Galactic and stellar structure

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