Geometrically thick tori around compact objects with a quadrupole moment

We study geometrically thick perfect-fluid tori with constant specific angular momentum, so-called "Polish doughnuts", orbiting deformed compact objects a quadrupole moment. More specifically, we consider two different asymptotically flat, static and axisymmetric vacuum solutions to Einstein's field equation non-zero moment, the q-metric Erez-Rosen spacetime. It is our main goal find features of Polish doughnuts in these spacetimes which qualitatively distinguish them from Schwarzschild As result that, for both metrics, there range positive (Geroch-Hansen) moments allows existence double tori. If fill their Roche lobes completely, meridional cross-section has shape fish, body fish corresponding outer torus fish-tail inner torus. Such do not exist