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Static spherically symmetric solutions to the Einstein-Euler equations withprescribed central densities are known to exist, be unique and smooth forreasonable equations of state. Some criteria are also available to decidewhether solutions have finite extent (stars with a vacuum exterior) or infiniteextent. In the latter case, the matter extends globally with the densityapproaching zero at infinity. The asymptotic behavior largely depends on theequation of state of the fluid and is still poorly understood. While a few suchunbounded solutions are known to be asymptotically flat with finite ADM mass,the vast majority are not. We provide a full geometric description of theasymptotic behavior of static spherically symmetric perfect fluid solutionswith linear and polytropic-type equations of state with index n>5. In order tocapture the asymptotic behavior we introduce a notion of scaledquasi-asymptotic flatness, which encodes a form of asymptotic conicality. Inparticular, these spacetimes are asymptotically simple.

On the asymptotic behavior of static perfect fluids