On the fluid ball conjecture
arXiv:2004.14240 · doi:10.1007/s10455-021-09786-1
Abstract
The fluid ball conjecture states that a static perfect fluid space-time is spherically symmetric. In this paper we construct a Robinson's divergence formula for the static perfect fluid space-time. Inspired by this conjecture, a rigidity result for the spatial factor of a static perfect fluid satisfying some boundary conditions is proved, provided that an equation of state holds.