Gravitating Scalarons with Inverted Higgs Potential

TL;DR

This paper introduces a new class of gravitating scalar solitons with positive mass by inverting the Higgs potential in Einstein--Klein--Gordon theory, avoiding phantom fields and connecting to black hole solutions.

Contribution

It demonstrates that scalarons with positive ADM mass can be achieved without phantom fields by inverting the Higgs potential, expanding the understanding of scalar solitons in gravity.

Findings

Scalarons with positive ADM mass are constructed without phantom fields.

The properties of these scalarons are systematically analyzed.

Connections to hairy black hole solutions are established.

Abstract

Previously, a class of regular and asymptotically flat gravitating scalar solitons (scalarons) has been constructed in the Einstein--Klein--Gordon (EKG) theory by adopting a phantom field with Higgs-like potential where the kinetic term has the wrong sign and the scalaron possesses the negative Arnowitt--Deser--Misner (ADM) mass as a consequence. In this paper, we demonstrate that the use of the phantom field can be avoided by inverting the Higgs-like potential in the EKG system when the kinetic term has a proper sign, such that the corresponding gravitating scalaron can possess the positive ADM mass. We systematically study the basic properties of the gravitating scalaron, such as the ADM mass, the energy conditions, the geodesics of test particles, etc. Moreover, we find that it can be smoothly connected to the counterpart hairy black hole solutions from our recent work in the small horizon limit.