Buchdahl's theorem

Buchdahl's theorem states that a static, spherically symmetric star with isotropic pressure and nonincreasing density must have a radius greater than nine-eighths of its Schwarzschild radius.

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Tolman–Oppenheimer–Volkoff equation: A relativistic hydrostatic-equilibrium equation relating pressure gradients, density, and enclosed mass in a spherical star. Buchdahl’s inequality is derived from the equations governing relativistic stellar equilibrium.
Hydrostatic equilibrium: A state in which pressure gradients balance forces such as gravity, preventing bulk motion. The theorem concerns stars held static by this balance.
Andréasson bounds: Compactness inequalities for static, spherically symmetric matter in general relativity under specified pressure conditions. These bounds generalize Buchdahl-type results to broader matter assumptions.
Neutron star: A compact stellar remnant composed primarily of densely packed neutrons and other subatomic matter. Neutron stars are tested against compactness bounds derived for relativistic stellar models.
Hans Adolf Buchdahl: A German-born theoretical physicist known for work on general relativity and exact solutions of gravitational field equations. He established the compactness theorem bearing his name.
Einstein field equations: Equations relating spacetime curvature to the distribution of matter and energy. They supply the gravitational field equations used in the theorem’s proof.
Perfect fluid: An idealized fluid whose stress-energy has isotropic pressure and no viscosity or heat conduction. Isotropic pressure in the theorem corresponds to this idealized matter model.
Causal compactness limit: An upper bound on neutron-star compactness imposed by causal equations of state. It is usually more restrictive for realistic matter than Buchdahl’s idealized limit.
Relativistic star: A star whose structure or gravity requires general relativity for an accurate description. Buchdahl’s result constrains this broader class of equilibrium models.
Relativistic stellar structure: The study of stars whose equilibrium and internal gravity are described using general relativity. Buchdahl’s theorem belongs to the mathematical theory of relativistic stellar models.