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 h^a with ordinary matter which is quantified by the introduction of an energy-momentum tensor field associated with ha. It is found that exist (i) a negative tangential pressure zone around low-mass distributions (μ < μ1) when the coupling constant a 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 μ < μ2; (iii) solutions that behave like those obtained from models with negative cosmological constant. In such a situation, the field ha plays the role of a cosmological constant.