This chapter briefly describes ‘perfect fluids’. These are characterized by their mass density ρ(t, xⁱ), pressure p(t, ⁱ), and velocity field v(t, ⁱ). The motion and equilibrium configurations of these fluids are determined by the equation of state, for example, p = p(ρ) for a barotropic fluid, and by the gravitational potential U(t, ⁱ) created at a point ⁱ by other fluid elements. The chapter shows that, given an equation of state, the equations of the problem to be solved are the continuity equation, the Euler equation, and the Poisson equation. It then considers static models with spherical symmetry, as well as polytropes and the Lane–Emden equation. Finally, the chapter studies the isothermal sphere and Maclaurin spheroids.
Keywords: self-gravitating fluids, perfect fluids, equation of state, gravitational potential, static models with spherical symmetry, polytropes, Lane–Emden equation, isothermal sphere, Maclaurin spheroids
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