The fluid ball conjecture for asymptotically flat static perfect fluid spacetimes

Let an asymptotically flat static perfect fluid spacetime be a solution satisfying the equations denoted by and. Fluid ball conjecture. Every such solution must be spherically symmetric. This is the fluid ball problem for static perfect fluid spacetimes; the supplied context points to related work on static uniqueness and asymptotic conditions, but does not establish the asserted spherical symmetry or resolve the problem.