Static solutions in Einstein-Chern-Simons gravity

TL;DR

This paper explores static solutions in five-dimensional Einstein-Chern-Simons gravity with generalized symmetries, analyzing the effects of an extra bosonic field coupled to matter, revealing pressure zones and cosmological-like behaviors.

Contribution

It introduces a study of static solutions with generalized symmetries in Einstein-Chern-Simons gravity, including the coupling of an extra bosonic field to matter and its effects.

Findings

Existence of negative tangential pressure zones around low-mass distributions.

Presence of a maximum tangential pressure in the outer regions.

Solutions mimic those with a negative cosmological constant, with the extra field acting as a cosmological constant.

Abstract

In this paper we study static solutions with more general symmetries than the spherical symmetry of the five-dimensional Einstein-Chern-Simons gravity. In this context, we study the coupling of the extra bosonic field $% h^{a}$ with ordinary matter which is quantified by the introduction of an energy-momentum tensor field associated with $h^{a}$. It is found that exist (i) a negative tangential pressure zone around low-mass distributions ($\mu <\mu_{1}$) when the coupling constant $\alpha $ is greater than zero; (ii) a maximum in the tangential pressure, which can be observed in the outer region of a field distribution that satisfies $\mu <\mu_{2}$; (iii) solutions that behave like those obtained from models with negative cosmological constant. In such a situation, the field $h^{a}$ plays the role of a cosmological constant.