The Spherical Symmetry of Static Stellar Systems in General Relativity

Abstract. A conjecture of many years standing in General Relativity is that static stellar models, under physically reasonable assumptions, must be spherically symmetric. Despite some real progress in the last eighteen years (Beig and Simon, Masood-ul-Alam) a proof of the conjecture, in its full generality, has remained elusive. We consider asymptotically flat, perfect fluid, static stellar spacetimes with minimal assumptions on the fluid. We require only that the density, ρ, and ρ + 6p (p is the fluid pressure) are non-negative. We impose no differential constraints on the density nor do we assume the exsistence of an equation of state. We do not require that there is only one star. We prove that such spacetimes are spherically symmetric.