On the derivations of the Equation of Hydrostatic Equilibrium

Abstract

We develop and present a geometrical and an analytical derivation of the equation of hydrostatic equilibrium in spherically symmetric stars with a generalized stress tensor. The analytical derivation is based on the Navier-Cauchy equation. We also critically examine the derivation of this equation found in textbooks on stellar astrophysics and show that there are errors in many of the derivations presented in textbooks.