As far as I know, as an object gets closer to an event horizon, gravitation time dilation makes it move slower from an outside perspective, so that it looks like it take an infinite amount of time for the object to reach the event horizon. It seems like a similar process should slow the formation of the black hole itself: As the star collapses, its gravitational time dilation make itself collapse more slowly.
This makes me wonder: from a perspective of an outside observer, can a singularity ever form?
E.g. someone on earth observers a massive star collapse, forming a black hole. From his perspective, the mass gets closer and closer, but does it ever form a singularity before the black hole evaporates?
Furthermore, if from a perspective of a mass collapsing into a black hole it’s time slows down and an outside universe “speeds up”, could this mean that the black hole evaporates before me, the mass, can become singularity?
In: Physics
A quick note on terminology; the “singularity” is the theoretical point right in the centre of a massive object where its density and gravitational field are infinite under current best models. They may exist, or the models may be not quite right (e.g. quantum mechanics may get in the way). Black holes may have singularities at their centre. But black holes don’t “need” singularities, they are defined by their event horizons.
The “event horizon” is the region around a black hole (technically a 2d surface) that makes a black hole special; it is the point where all worldlines (so future paths in spacetime – where things *could* go) of objects in that region end up falling down towards the massive object in the middle (see [this neat set of diagrams](https://en.wikipedia.org/wiki/File:BH-no-escape-1.svg)). In the simple model for a black hole, the event horizon is a distance of 2GM/c^2 from the singularity (where G is the gravitational constant, M the total mass inside the event horizon and c the ‘speed of light’).
A black hole forms when there is enough mass within a small enough volume so that this distance (2GM/c^(2)) is outside the object. All that mass doesn’t have to be concentrated at the singularity, it just has to be within the event horizon distance of it.
At the event horizon, from the perspective of an observer an infinite distance away, time dilation would be infinite. So when observing something fall into a black hole, you can never see the object cross the event horizon, it will just slow down and stop (and you can obviously never see it cross, as the light of it crossing can never reach you).
But locally everything looks normal. From the perspective of an object falling into the black hole, it doesn’t notice the event horizon (although they’ll be a lot of other stuff going on there – it won’t be a friendly place to hang out), it just keeps falling. [This graphic shows this fairly well](https://en.wikipedia.org/wiki/File:Gravitational_time_dilation_around_a_black_hole.gif) – on the left you have what things look like from the object’s perspective as it falls in. On the right you have the outside observer’s view. From the object’s point of view, it just falls in as normal.
Of course, *this only applies once the black hole has formed*, so once the event horizon exists. Before then, the time dilation in that region, while significant, wouldn’t be infinite. So there would still be time for things to fall in.
Disclaimer; I haven’t done the maths (GR maths is notoriously difficult), but I suspect that yes, if you were an infinite distance away, it would take an infinite amount of time for a black hole to form. But if you are an infinite distance away none of that matters – you are too far away. If you are any closer (i.e. a finite distance away), it would take less than an infinite amount of time to form – and so it is possible.
And we know this is possible; black holes exist.
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