A remote observer describes a black hole with Schwarzschild coordinates. These have a coordinate singularity at the horizon, which implies that the distante between any spacetime point and the horizon is infinite. My question is whether a remote observer is allowed to claim that a black hole may increase its mass (objects falling into the black hole), since any object needs of infinite time to reach the horizon. (Example: we as remote observers of the supermassive black hole in the centre of the Milky Way). Regards.