Static Spherically Symmetric Einstein-aether models: Integrability and the Modified Tolman-Oppenheimer-Volkoff approach

We study the evolution of the dynamics and the existence of analytic solutions for the field equations in the Einstein-aether theory for a static spherically symmetric spacetime. In particular, we investigate if the gravitational field equations in the Einstein-aether model in the static spherically symmetric spacetime possesses the Painleve property, so that an analytic explicit integration can be performed. We find that analytic solutions can be presented in terms of Laurent expansion only when the matter source consists of a perfect fluid with linear equation of state (EoS) $\mu =\mu _{0}+\left( \eta -1\right) p,~\eta >1$. In order to study the evolution of the dynamics for the field equations we apply the Tolman-Oppenheimer-Volkoff (TOV) approach. We find that the relativistic TOV equations are drastically modified in Einstein-aether theory, and we explore the physical implications of this modification. We study perfect fluid models with a scalar field with an exponential potential. We discuss all of the equilibrium points and discuss their physical properties.