Imagine a star emitting light, and collapsing to form a black hole. As seen from someone riding the surface of this star, it will only take a few hours for it to fall inside its Event Horizon. As seen from far away, there will come a moment when the last photon emitted by the star has been emitted by the the star's surface when it was just outside the event horizon. When this last photon reaches you at an enormous redshift, the light from the star will have been extinguished. But the amazing thing about the infall process is that you will receive that last photon thousands or even millions of years in the future.
The surface of the star, as seen from your vantage point, may take an enormous amount of time to actually fall inside its horizon, but as seen from the surface of the star, it only takes a few seconds. Black holes, to the external observer, are what physicists call an 'asymptotic' solution to general relativity, which means that they may technically take an eternity to form in our rest frame, but they form nevertheless because the physics of the freely falling observer will see this event as a very well defined and fatal one that takes only a few hours to occur.
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