Extensions of the Penrose inequality with angular momentum

We numerically investigate the validity of recent modifications of the Penrose inequality that include angular momentum. Formulations expressed in terms of asymptotic mass and asymptotic angular momentum are contradicted. We analyzed numerical solutions describing polytropic stationary toroids around spinning black holes.
Comment: Revised and expanded: a new Section 3 on numerical integration; misprints corrected; minor stylistic changes. Conclusions are unchanged