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.
Facts
StatementFor static, spherically symmetric matter configurations under certain conditions, the mass must satisfy an inequality with the areal radius, Buchdahl's bound, expressing a maximal sustainable density for ordinary gravitating matter. 2 Classification
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Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Sources
1. Wikipedia: Buchdahl's theorem
WikipediaLead section, statement-form referenceQuote, Lead section, statement-form reference
In general relativity, Buchdahl's theorem, named after Hans Adolf Buchdahl, makes more precise the notion that there is a maximal sustainable density for ordinary gravitating matter.
2. Buchdahl's theorem, Wikipedia
Lead paragraphQuote, Lead paragraph
It gives an inequality between the mass and radius that must be satisfied for static, spherically symmetric matter configurations under certain conditions.
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