Static solutions in Einstein-Chern-Simons gravity

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 $$ 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.