The Tolman–Oppenheimer–Volkoff equation governs a static, spherically symmetric perfect fluid in general relativity. In geometrized units, if is the mass inside areal radius , then
The interior Schwarzschild metric is the exact static solution for a spherical fluid of constant density. If the star has mass and radius , its pressure is
Buchdahl's theorem gives for a static spherical perfect-fluid star whose density is nonincreasing outwards, subject to its regularity assumptions. Equality would require divergent central pressure, so every regular such star satisfies .
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The Tolman–Oppenheimer–Volkoff (TOV) equation is a key result in general relativity that describes the structure of a spherically symmetric, non-rotating star in hydrostatic equilibrium, particularly those composed of nuclear matter, such as neutron stars. It extends the concepts of hydrostatic equilibrium in a gravitational field, taking into account the effects of general relativity.