Neutron stars in the theory of gravity with non-minimal derivative coupling in the presence of a scalar field charge. Analysis of the equations of state and solutions for the scalar field

We consider neutron stars in the theory of gravity with a non-minimal derivative coupling of the scalar field and the Einstein tensor in the presence of a charge Q of the scalar field. In this paper we consider model polytropic and realistic equations of state of neutron matter. It is shown that regardless of the type of the equation of state, the scalar field becomes complex in the case Q≠0, which possibly indicates about instability of the solution with a charged scalar field. This paper also discusses the properties of the equations of state related to restrictions on the sound speed.