The angular momentum and mass formulas for rotating stationary quasi-black holes

We consider the quasi-black hole limit of a stationary body when its boundary approaches its own gravitational radius, i.e., its quasi-horizon. It is shown that there exists a perfect correspondence between the different mass contributions and the mass formula for quasi-black and black holes in spite of difference in derivation and meaning of the formulas in both cases. For extremal quasi-black holes the finite surface stresses give zero contribution to the total mass. Conclusions similar to those for the properties of mass are derived for the angular momentum.