# Are Black Holes Theoretical Phantoms?

I understand that it takes an infinite amount of time for an event horizon to form. Give this, if there are any black holes, they have been around forever.

Are there good comological models that include 'forever', or is my premise wrong?

## Answers and Replies

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Hurkyl
Staff Emeritus
Gold Member
I understand that it takes an infinite amount of time for an event horizon to form.
How are you measuring that?

A watch falling into a collapsing star would measure a finite amount of time before it reaches the event horizon. OTOH the photons emitted from the watch as it passes through would take an "infinite" amount of time to reach an external observer. (According to GR)

How are you measuring that?

A watch falling into a collapsing star would measure a finite amount of time before it reaches the event horizon. OTOH the photons emitted from the watch as it passes through would take an "infinite" amount of time to reach an external observer. (According to GR)
Anywhere that is always outside an event horizon. The syntax can get sticky, here, but if there is no event horizon, there is no watch that will ever fall through it. But this is a distraction.

We are on Earth. There may be a collapsing star somewhere, at a distance larger than it's Schwarzschild radius. Would it ever form an event horizon according to our local, normal coordinates?

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Hurkyl
Staff Emeritus
Gold Member
We are on Earth. There may be a collapsing star somewhere, at a distance larger than it's Schwarzschild radius. Would it ever form an event horizon according to our local, normal coordinates?
Yes -- an infalling watch measures a finite amount of time before hitting a horizon, and therefore the horizon would be contained in any Riemann normal 'coordinate chart' centered on Earth.

(Assuming, of course, that expansion or other gravitational effects do not prevent geodesic travel from Earth to the star. But, I suppose if that's happened, the star has already fallen off the 'coordinate chart', and so the question would be moot)

(Also making the usual assumptions that there isn't an 'edge of the universe' at which geodesics would vanish before reaching the alledged star and what not)

(I'm putting 'coordinate chart' in quotes, because Riemann normal coordinates do not meet the criteria demanded of coordinate charts in differential geometry -- namely that distinct coordinates always refer to distinct points)

Thank you Hurkyl.

Things are stranger than I was prepared for. It appears that seemingly contrary statements such as 'never happened' vs 'happened', or 'will happen' vs 'will not happen' are contectual. I had thought this sort of thing was confined within the domain of quantum mechanics and not relativity.

Chronos
Gold Member
Observationally, black holes are very real. Particles may not be real, but, deceivingly convincing. If you get too near a particle, it has properties that look like a singularity.

If you get too near a particle, it has properties that look like a singularity.
what do you mean by this? i'm not very familiar with QM nor GR, but i'm about to start these subjects next semester.. it what sense do you 'approach' a particle? and what are the similiarities with a black hole?
i first agreed with the "particles may not be real" statement, since the atom has no definite boundary (i'm clueless about tinier particles), so it's kinda hard to talk about 'the' particle.. or maybe in the sense that the atoms are made up of even smaller things, and who knows, maybe they're in turn made up of EVEN smaller things..

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I see evidence of infalling matter, Chronos. Not black holes.

Dmitry, Then how can one speak of existance?

Phrak, the word 'exists' is too fuzzy in the curved spacetime.
when we say 'it exists now' we speak about space-time relation. Or zero-interval in the past, when we talk about distant stars. Or we mean that we can come and touch that object, which means, that there are some timelike trajectories which intersect with that object.

No 'now' surface intersects with an interior of the black hole, so no, black holes do not exist.
But there are some spacelike trajectories which intersect with it (you can fly into the black hole) so yes, black holes do exist :)

Hurkyl
Staff Emeritus
Gold Member
Phrak, the word 'exists' is too fuzzy in the curved spacetime.
Surely, introducing even fuzzier terms doesn't help clear things up. :tongue: I have no idea what you mean by a "'now' surface".

And I don't see your problem with "exists" -- either there is such an object in space-time or there is not, there is no mathematical ambiguity there. Phrak's original question, I think, simply boils down to the fact that coordinate charts need not cover all of space-time.

But there are some spacelike trajectories which intersect with it (you can fly into the black hole) so yes, black holes do exist :)
That's a timelike trajectory....

That's a timelike trajectory....
Yes, sorry, I was drunk :) Sunday...

Chronos