Von Zeipel theorem

In a uniformly rotating, radiative star in hydrostatic equilibrium, the radiative energy flux is proportional to effective gravity. This makes the poles brighter and hotter than the equator.

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Effective gravity: The local acceleration experienced in a rotating frame after gravitational and centrifugal accelerations are combined. Its variation across a rotating star sets the local radiative flux.
Stellar structure: The study of how a star’s internal pressure, temperature, density, and energy transport vary. The theorem is a result about equilibrium structure in rotating stars.
Oblate star: A star whose rotation makes its equatorial radius larger than its polar radius. Its shape produces latitude-dependent effective gravity and flux.
Lucy gravity-darkening law: An empirical gravity-darkening relation for convective stars, with a weaker flux dependence on effective gravity. It replaces the classical radiative prediction for stars with convective envelopes.
Radiative diffusion: The transport of energy through matter by repeated absorption and re-emission of photons. The theorem follows when radiation carries energy through the star’s envelope.
Uniform rotation: Rotation in which all parts of an object share the same angular velocity. Uniform angular velocity is one of the theorem’s defining assumptions.
Altair: A rapidly rotating star in the constellation Aquila, observed to be flattened and gravity-darkened. Its interferometric images show the pole-to-equator brightness variation associated with the theorem.
Espinosa Lara–Rieutord gravity-darkening law: A gravity-darkening model for rapidly rotating stars that accounts for departures from simple radiative equilibrium. It improves on the classical relation when rotation is strong.
Hydrostatic equilibrium: A state in which pressure gradients balance forces acting on a fluid. Its balance in a rotating star helps make flux track effective gravity.
Radiative zone: A stellar region where energy is transported mainly by radiation rather than convection. The theorem applies where radiative transport governs the energy flow.