Buchdahl's Theorem

Buchdahl's theorem, named for Hans Adolf Buchdahl, is a result in general relativity that makes precise the idea that ordinary gravitating matter has a maximum sustainable density. For a static, spherically symmetric body of a given areal radius, the theorem gives an inequality the body's mass must satisfy under fairly general conditions, so a body that violated the bound couldn't exist as an ordinary static star. The bound, often called Buchdahl's bound, had already been noted by Karl Schwarzschild for the special case of a constant-density fluid, though it shouldn't be confused with the much smaller Schwarzschild radius.