*Article* **Inflation inside Non-Topological Defects and Scalar Black Holes**

#### **Yves Brihaye 1, Felipe Console 2 and Betti Hartmann 2,3,4,\***


Received: 29 October 2020; Accepted: 25 November 2020; Published: 22 December 2020

**Abstract:** In this paper, we demonstrate that a phenomenon described as *topological inflation*, during which inflation occurs inside the core of topological defects, has a non–topological counterpart. This appears in a simple set-up containing Einstein gravity coupled minimally to an electromagnetic field as well as a self-interacting, complex valued scalar field. The U(1) symmetry of the model is unbroken and leads to the existence of globally regular solutions, so-called boson stars, that develop a horizon for sufficiently strong gravitational coupling. We also find that the same phenomenon exists for black holes with scalar hair.

**Keywords:** black holes; scalar fields; boson stars
