As far as I know, the time dilation at the event horizon of a black hole is infinite, so everything falls asymptotically towards, but never reaching, the horizon for an outside observer. How then can a black hole gain in mass for this observer?

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    $\begingroup$ If you shake the BH, it feels more massive because of the stuff sticking to the horizon. If you shoot a surface grazing laser beam on the BH, the beam deflects further away from the BH because of the stuff on the horizon. If you measure the Hawking radiation, it's redshifted because of the gravity of the stuff in the horizon. The BH looks and feels like a BH with more mass. $\endgroup$ – stuffu Jan 23 '15 at 21:33