Could time move inside a black hole?

[whatdoctor]

At the event horizon for a black hole is R=2GM/C^2
This means that, as a star collapses, it gets more dense until this limit is reached. Assuming a consistent density (just an approximation as I know this will not really be the case), the Mass will reduce proportionally to the cube of R, but the event horizon goes down proportional to M - so the event horizon radius reduces faster than the mass that would create it. This means that, below the event horizon, time is still moving.
Assuming the minimum size of a naturally occurring black hole is about 2 stellar masses - this gives us a radius of about 6km inside every black hole where time still moves.
Or does the star instantaneously collapse to a singularity? If so, how can it continue to collapse once time has stopped?

 

[Drakkith]

Assuming a consistent density (just an approximation as I know this will not really be the case), the Mass will reduce proportionally to the cube of R, but the event horizon goes down proportional to M - so the event horizon radius reduces faster than the mass that would create it. This means that, below the event horizon, time is still moving.

Time would pass normally for any observer who passes the event horizon. It's the rate that the observer's time passes as viewed from someone well outside the event horizon that goes to zero. That is, to an observer standing far away from the black hole, the rate at which an infalling observer's clock ticks approaches zero as they approach the event horizon. The problem with black holes is that thing become unpredictable when an observer reaches the singularity.

Or does the star instantaneously collapse to a singularity? If so, how can it continue to collapse once time has stopped?

I believe there is an issue with how an event horizon can form if the infalling material slows down under time dilation. As the density during collapse increases, the amount of time dilation increases, so to an far away observer the material should appear to "freeze" before an event horizon forms. I'm not sure if this is a real issue or if there is a way around it. Perhaps someone else can answer that.

 

[Chronos]

Given it is presumed that space collapses to zero volume at the singularity, it is perfectly reasonable to expect the very concept of time itself also vanishes at the singularity. Nonsensical situations like this is what leads most scientists to reject the notion of the physical existence of singularities

 

[PeterDonis]

Assuming a consistent density (just an approximation as I know this will not really be the case), the Mass will reduce proportionally to the cube of R

No, it won't. The mass of the collapsing object is constant (assuming it doesn't give off radiation or eject matter--any real collapse will do both of those things, but we can idealize them away for this discussion).

so the event horizon radius reduces faster than the mass that would create it

No, this is not correct. Assuming an idealized collapse that does not emit radiation or eject matter, the horizon radius is known at the start of the collapse--it's the radius corresponding to the original mass of the collapsing object.

This means that, below the event horizon, time is still moving.

It is true that "time is still moving" below the horizon, in the sense that objects that fall in (or objects in the collapsing matter) continue to experience time normally. So you have the right conclusion here, but your method of getting to it is incorrect. See above.

 

[whatdoctor]

I would say that an object cannot fall past the event horizon. My reasoning is this: From the perspective of the object falling, time moves normally for it - but time outside the event horizon would appear to speed up. So as the next second passes for the falling object, billions (or even trillions) of years pass outside the event horizon. By this time the black hole would cease to exist (by Hawking radiation). So as soon as the object hits the event horizon, the black hole vanishes.

 

[phinds]

I would say that an object cannot fall past the event horizon. My reasoning is this: From the perspective of the object falling, time moves normally for it - but time outside the event horizon would appear to speed up. So as the next second passes for the falling object, billions (or even trillions) of years pass outside the event horizon. By this time the black hole would cease to exist (by Hawking radiation). So as soon as the object hits the event horizon, the black hole vanishes.

Totally incorrect. Have you been reading this thread? The infaller doesn't even notice the EH.

 

[PeterDonis]

From the perspective of the object falling, time moves normally for it - but time outside the event horizon would appear to speed up

No, it doesn't. Don't confuse the infaller with a static observer. A static observer, one who "hovers" at a constant altitude close to the horizon, will see the rest of the universe speeded up, yes. But an infalling observer will not. In fact, as the infalling observer crosses the horizon, he will see the rest of the universe slowed down.