It is known since Hawking that an observer "a rest" at some far distance of a black hole sees a thermal radiation emitted by the black hole. The mass of the black hole diminishes while it emmits the thermal flow of particles. For a free falling observer there is no thermal radiation. So, for him the mass of the black hole may not diminish; it may remains constant. However, the mass should be a well defined observable for both observers, so that they should agree with their observed value of the mass. Can someone help to understand this paradox ?