You Cannot Press Out the Black Hole

It is shown that a ball-shaped black hole region homeomorphic with Dn cannot be pressed out, along whichever axis penetrating the black hole region, into a black ring with a doughnut-shaped black hole region homeomorphic with S1 x D**(n-1). A more general prohibition law for the change of the topology of black holes, including a version of no-bifurcation theorems for black holes, is given.