Abstract
Context. We study jets using a semi-analytical model of the general relativistic magnetohydrodynamic (GRMHD) equations in the Kerr metric that describes them near the rotation axis, assuming a steady state, and axisymmetry. Aims. The goal is to model the inner spine of a relativistic jet in order to solve for the bulk acceleration and the shape of the jet and understand how these quantities depend on the enthalpy and the magnetic field. Methods. The model is constructed by expanding the rotating black hole metric and forces with respect to the polar angle about the rotation axis. This results in a system of ordinary differential equations that determine the dependence on the radial distance. The difference with previous semi-analytical models that expand the metric around the rotation axis is that the flow is governed by a polytropic equation of state. Results. The solutions in this work start from a stagnation surface very close to the event horizon and become highly relativistic, achieving large Lorentz factors at large distances.
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