# Is time stopped inside a black hole?

## Main Question or Discussion Point

Greetings,

Due to extreme time dilation by gravity, is time stopped or nearly stopped inside the event horizon of a black hole?

I'm guessing it is stopped completely at the singularity and nearly standing still around it? So once a black hole forms, next to no time passes and next to nothing happens in it? Billions of years pass outside but just a few moments inside?

Thanks

Jonathan Scott
Gold Member
Greetings,

Due to extreme time dilation by gravity, is time stopped or nearly stopped inside the event horizon of a black hole?

I'm guessing it is stopped completely at the singularity and nearly standing still around it? So once a black hole forms, next to no time passes and next to nothing happens in it? Billions of years pass outside but just a few moments inside?

Thanks
Depends on the point of view.

From the point of view of a static external coordinate system, time is spacelike inside the event horizon. I've heard various attempts to explain what that really means, but I didn't find any of them very satisfactory.

From the point of view of a free falling observer, time carries on as normal but the observer will hit the singularity in a finite time.

Chalnoth
Depends on the point of view.

From the point of view of a static external coordinate system, time is spacelike inside the event horizon. I've heard various attempts to explain what that really means, but I didn't find any of them very satisfactory.
Well, in large part this just means that the Schwarzschild coordinates are bad coordinates at or inside the event horizon of a black hole. This is one of the problems in General Relativity: in a curved space time, it actually isn't possible to use one single coordinate system everywhere.

In GR classes, one common example used to illustrate this point is the surface of a sphere, like the Earth's surface. It isn't actually possible to use one single, well-behaved coordinate map for the entire sphere: you need at least two. If you use the normal spherical coordinates, for example, your calculations start to go wonky at the poles, as the latitude coordinate can take many values that all represent the same point.

Here is a thought experiment that might show what is happening: How fast does time in the rest of the universe seem to be passing from a viewpoint inside the black hole? You can't see in, but you can see out, right?

Freely falling observer sees the universe outside *slowing down* based on the light he/she receives

The concept of time dilation when you can't come back and sync your clocks is difficult to be defined.

Finally, observer can't be at rest inside BH and has very short lifespan.

Chronos
Gold Member
The passage of time is believed to slow to zero at the event horizion, which suggests time runs backwards inside the event horizon. Something is probably amiss.

zonde
Gold Member
From the point of view of a static external coordinate system, time is spacelike inside the event horizon. I've heard various attempts to explain what that really means, but I didn't find any of them very satisfactory.
I would say that using coordinate system of some external observer object inside event horizon should move faster then speed of light in order to exist. That is what spacelike time would mean.

So answering OP question I would say that time is not stopped but you can't be at rest relative to event horizon. If you will try to mark a spot that is inside event horizon and is at rest you will simply get causally unrelated series of event at this spot.

The passage of time is believed to slow to zero at the event horizion, which suggests time runs backwards inside the event horizon. Something is probably amiss.
The count of a local clock as it approaches the event horizon, slows to zero changes as its duration approaches infinity which should coincide with the singularity.

Chalnoth
The count of a local clock as it approaches the event horizon, slows to zero changes as its duration approaches infinity which should coincide with the singularity.
Well, the image of the clock does appear to stop to an outside observer as it crosses the event horizon, but this is largely just because it is an event horizon, not because anything special is happening there. From the perspective of the clock, nothing particularly funny happens at the event horizon.

Freely falling observer sees the universe outside *slowing down* based on the light he/she receives
Agreed

Finally, observer can't be at rest inside BH and has very short lifespan.
A freely falling observer is at rest. I think what you mean is that an observer, freely falling or not, cannot halt his fall inside the EH.

Well, the image of the clock does appear to stop to an outside observer as it crosses the event horizon, but this is largely just because it is an event horizon, not because anything special is happening there. From the perspective of the clock, nothing particularly funny happens at the event horizon.
Agreed, a second is still a second locally, I was just pointing out that time does not stop just because the length of a duration between clocks is changing. :shy:

Chronos
Gold Member
External clocks appear to speed up as a free falling observer approaches the event horizon of a black hole.

External clocks appear to speed up as a free falling observer approaches the event horizon of a black hole.
Yea, that's what I thought. Would someone falling in witness the end of the universe? ( disregarding that he dies from being stretched )

George Jones
Staff Emeritus
Gold Member
External clocks appear to speed up as a free falling observer approaches the event horizon of a black hole.
No, external clocks appear to slow down as a free falling observer approaches the event horizon of a black hole.
2. Suppose that observer A hovers at a great distance from a black hole, and that observer B hovers very close to the event horizon. The light that B receives from A is tremendously blueshifted. Now suppose that observer C falls freely from a great distance. C whizzes by B with great speed, and, just past B, light sent from B to C is tremendously Doppler reshifted. What about light from A to C. The gravitation blueshift from A to B is less that the Doppler redshift from B to C. As C crosses the event horizon, C sees light from distant stars redshifted, not blueshifted.

2. Suppose that observer A hovers at a great distance from a black hole, and that observer B hovers very close to the event horizon. The light that B receives from A is tremendously blueshifted. Now suppose that observer C falls freely from a great distance. C whizzes by B with great speed, and, just past B, light sent from B to C is tremendously Doppler reshifted. What about light from A to C. The gravitation blueshift from A to B is less that the Doppler redshift from B to C. As C crosses the event horizon, C sees light from distant stars redshifted, not blueshifted.
Let's simplify this example a little and ignore B. C begins his freefall towards a BH at A and the light C is measuring the redshift or blueshift of also originates at A. It seems intuitive that the redshift due to C's velocity away from A due to gravitational acceleration should be be equal to the blueshift of the light from A at C also due to gravitational acceleration thus C would not measure either redshift or blueshift. Why would this not be so?

No, external clocks appear to slow down as a free falling observer approaches the event horizon of a black hole.
Wouldn't that depend of the angle between clock and observer? Clocks "above" the observer would appear to slow down, but clocks peprpendicular to the free falling trajectory would speed up. Or am I dead wrong?

Time slows down near a gravity source, but to the observer near a gravity source, it seems like it speeds up.

Chronos
Gold Member
Kudos to George. Given the infalling observer appears time dilated to an external observer the infalling observer approaches the event horizon, it appears logical the external observer should be time contracted from the perspective of the infalling observer - but, this is illogical. As the infalling observer approaches the event horizon, photons from the external universe require an increasingly longer 'time' interval to reach the infalling observer. So, the infalling observer passes the event horizon with a very ordinary perception of the passage of time in the external universe. I need a cold, wet towel to wrap around my head.

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Kudos to George. Given the infalling observer appears time dilated to an external observer the infalling observer approaches the event horizon, it appears logical the external observer should be time contracted from the perspective of the infalling observer - but, this is illogical. As the infalling observer approaches the event horizon, photons from the external universe require an increasingly longer 'time' interval to reach the infalling observer. So, the infalling observer passes the event horizon with a very ordinary perception of the passage of time in the external universe. I need a cold, wet towel to wrap around my head.
I've tried a cold towel before and it does not help. Next question I have is which direction does a accelerometer point, and at which point will it change, for the in falling observer?

Chalnoth
I've tried a cold towel before and it does not help. Next question I have is which direction does a accelerometer point, and at which point will it change, for the in falling observer?
A pointlike infalling observer would, by definition, always read zero on an accelerometer.

Here are a couple of truely astonishing facts about Sagittarius A* and the central super massive black hole:

Its mass is 4.31 ± 0.38 million solar masses yet its diameter is 44 million Kms, approximately the same as the orbit of mercury. (I think this must be the Schwarzschild diameter)

There are several thousand stars within 3 light years of the black hole. ie. Slightly less that the distance to our nearest star Alpha Centauri.

http://en.wikipedia.org/wiki/Sagittarius_A*

I would imagine that anyone who happens to find themselves anywhere near the area must be pretty concerned!

Interestingly, the Schwarzschild diameter in the link below is stated to be 26.6 Million Kms, perhaps the latter figure was meant to be the accretion disk diameter.

Also given that we are only 26,000 light years from all these high energy events it is very easy to see how gamma energy could wreak havoc here and cause species extinctions.

Then there are the hypervelocity stars traveling at up to 0.5c to contend with.
One example is Kapteyns star travelling at just under 0.1c at a distance of 13 light years away! It got to within 7 light years 10,800 years ago so we are good!

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In haste I missed off the % symbols on the speeds of hyper velocity stars!

Then there are the hypervelocity stars traveling at up to 0.5%c to contend with.
One example is Kapteyns star travelling at just under 0.1%c at a distance of 13 light years away.

Chalnoth
In haste I missed off the % symbols on the speeds of hyper velocity stars!

Then there are the hypervelocity stars traveling at up to 0.5%c to contend with.
One example is Kapteyns star travelling at just under 0.1%c at a distance of 13 light years away.
That makes more sense :)

Couple more interesting facts about supermassive black holes:

Their mass is about 0.5% of their host galaxy mass. The two are related, as is their mass which is proportional to the galaxy rotation speed.

It is believed that Supermassive black holes formed first out of the collapse of the gas that eventually forms the rest of the galaxy. Perhaps it was also a short lived massive star for a few million years?

Once formed they become quasars as the gas falls in and the radiation helps to create the star birth all over the galaxy.

Once they reach a certain size the quasar radiation blows the material away from the center and they stop radiating.

At the center of our galaxy is an estimated 10,000 stellar black holes which are eventually going to be absorbed by the supermassive black hole.

Seems like we really do owe existence to the monster called Sagittarius A* and it has been there since the beginning and created our galaxy out of the primordial gas.

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A primordial black hole is a hypothetical type of black hole that is formed not by the gravitational collapse of a large star but by the extreme density of matter present during the universe's early expansion. According to the Big Bang Model, during the first few moments after the Big Bang, pressure and temperature were extremely great. Under these conditions, simple fluctuations in the density of matter may have resulted in local regions dense enough to create black holes. Although most regions of high density would be quickly dispersed by the expansion of the universe, a primordial black hole would be stable, persisting to the present.

http://en.wikipedia.org/wiki/Primordial_black_hole

So is it correct then that Primordial black holes could have been responsible for the central black hole in our galaxy and all the others and hence their formation?

Are Primordial black holes still believed to be consistant with the latest inflation theories?

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