Generating solutions for charged stellar models in general relativity

It is shown that the expressions for the tangential pressure, the anisotropy factor and the radial pressure in the Einstein-Maxwell equations may serve as generating functions for charged stellar models. The latter can incorporate an equation of state when the expression for the energy density is also used. Other generating functions are based on the condition for the existence of conformal motion (conformal flatness in particular) and the Karmarkar condition for embedding class one metrics, which do not depend on charge. In all these cases the equations are linear first order differential equations for one of the metric components and Riccati equations for the other. The latter may be always transformed into second order homogenous linear differential equations. These conclusions are illustrated by numerous particular examples from the study of charged stellar models.

Automated summary

The expressions in the Einstein-Maxwell equations serve as generating functions for charged stellar models, incorporating equation of state and conformal motion conditions. The resulting equations are linear first order differential equations and Riccati equations, which can always be transformed into second order homogeneous linear differential equations.