I was reading some questions and answers about black holes and whether matter can actually pass through the apparent horizon, in particular this one:
It seems that the argument that matter slows down and never passes the apparent horizon is similar to Zeno's paradox Achilles and the tortoise. Due to the effects of the immense gravity a photon emitted by the matter travelling away from the black hole get red shifted and from its perspective takes longer to reach our hypothetical observer than if the black hole was not there. At some point it will take 10 times as long to reach us than normal, then there will be a point at which it takes 100 times as long, then 1000 times and so on. If you keep measuring infinitesimally smaller increments you can keep this progression going forever since at precisely the apparent horizon it will take a photon travelling exactly away from the black hole an infinite amount of time to reach us.
However, as far as I can see, all this remains true if the object accelerates towards the black hole as viewed from some outside time frame. Due to time dilation effects it will appear to an in-Universe observer that the object never quite reaches the apparent horizon yet it seems to me that an outside Universe observer would see the object pass through and merge with the mass at the centre of the black hole very quickly.
Are both views correct or does it not make sense to contemplate the Universe from outside the Universe? If we were able to measure the gravity of the object directly and separately from the remaining mass of the black hole would we be able to detect that the matter had indeed passed the apparent horizon?