Static spherically symmetric Einstein-æther models II: Integrability and the modified Tolman–Oppenheimer–Volkoff approach

Abstract

We investigate the existence of analytic solutions for the field equations in the Einstein-æther theory for a static spherically symmetric spacetime and provide a detailed dynamical systems analysis of the field equations. In particular, we investigate if the gravitational field equations in the Einstein-æther model in the static spherically symmetric spacetime possesses the Painlevè property, so that an analytic explicit integration can be performed. We find that analytic solutions can be presented in terms of Laurent expansions only when the matter source consists of a perfect fluid with a linear equation of state (EoS) μ=μ0+h−1p,h>1. In order to study the field equations we apply the Tolman–Oppenheimer–Volkoff (TOV) approach and other approaches. We find that the relativistic TOV equations are drastically modified in Einstein-æther 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.