What happens to acceleration when you approach a singularity?

[uruk]

I was wondering what happens to acceleration as you approach the singularity of a black hole?

Acceleration is dependent on gravity according to Newton. If gravity increases to infinity at the singularity what happens to an objects acceleration as it approaches the singularity?
Would the object's acceleration also approach infinity? What would that mean?

I tried looking this up at a couple of sites. The nearest thing to an answer I found was that Newtonian physics breaks down after you get past the event horizon where escape velocity exceeds the speed of light.

Would relativity be any help?

 

[Gord_in_Toronto]

Acceleration is dependent on gravity according to Newton.

That may be your problem right there.

I think an examination of the expression "frame of reference" may be a start. But I'll wait for a real astrophysicist to show up.

 

[uruk]

I think I may see my problem. Newton uses the universal gravitational constant. I guess what I meant was standard gravity or the local acceleration due to gravity.

Little "g"(the nominal acceleration due to local gravity) is dependent on big "G"(universal gravitational constant) and the mass of the attracting object.
http://en.wikipedia.org/wiki/Standard_gravity

Little "g" would seem to increase if the mass of the attracting body increases and the radius decreases. A singularity mass increases (and thus gravitational field) presumably to infinity and its radius decreases (also presumably to infinity).

What happens to little "g" under those circumstances?

Either accleration increases to infinty (whatever that means) or the formula breaks down (doesn't apply).

 

[Reality Check]

If gravity increases to infinity at the singularity what happens to an objects acceleration as it approaches the singularity?

Gravity does not increase to infinity at the singularity.
The force due to gravity is caused by the mass of the object. For a black hole singularity this mass just happens to be packed into an infinitesimal volume.

So according to Newton, the acceleration is constant. GR may differ.

 

[Trent Wray]

Perhaps check this page out ... farther down the page it says that at 0.35 Schwarzschild radii, relative to observers freely falling radially from rest at infinity, our velocity increases towards the speed of light.

 

[sol invictus]

I was wondering what happens to acceleration as you approach the singularity of a black hole?

Acceleration is dependent on gravity according to Newton. If gravity increases to infinity at the singularity what happens to an objects acceleration as it approaches the singularity?
Would the object's acceleration also approach infinity? What would that mean?

I tried looking this up at a couple of sites. The nearest thing to an answer I found was that Newtonian physics breaks down after you get past the event horizon where escape velocity exceeds the speed of light.

Would relativity be any help?

When you're freely falling through a gravitational field you don't feel any force - you float around inside your spaceship like an astronaut. The only exception to that is what are called tidal forces - if the gravity field varies in strength across space, different parts of your body will try to accelerate at different rates, which means you'll feel a tugging as your body holds itself together (this effect is what causes the tides on earth, so these forces are called tidal forces).

As you approach a singularity, the variation in the gravity field gets stronger and stronger, and the mlld tugging you were feeling will grow stronger and stronger. Before you could actually touch the singularity your body would be torn apart by these forces.

As for what happens at the singularity itself, no one knows - it's a place where the laws of general relativity (Einstein's theory of gravity) break down, and it isn't clear what (if anything) should replace them.

As for the horizon - for a large black hole, the horizon is actually completely regular. Tidal forces are weak, and you wouldn't notice anything special as you fell into it.

 

[Illustronic]

I'm one that has a real problem with singularity being infinitely small like an atom. I understand the space particles are separated by in atoms, but everything we can detect in the size of a single atom, common now.

It must be an expression of state of matter in intense heat before it formed matter mass, formed time, thus formed space to expand in.

The big bang stops me at that tiny point in space. I can't except all things can compress that much. Not infinitesimally tiny.

Sorry if this is off topic.

 

[sol invictus]

I'm one that has a real problem with singularity being infinitely small like an atom. I understand the space particles are separated by in atoms, but everything we can detect in the size of a single atom, common now.

It must be an expression of state of matter in intense heat before it formed matter mass, formed time, thus formed space to expand in.

The big bang stops me at that tiny point in space. I can't except all things can compress that much. Not infinitesimally tiny.

Sorry if this is off topic.

Not really off topic - a black hole singularity is very similar to the big bang singularity (except it's in your future, if you fall in, rather than your past). And you may be correct. We don't know what happens, not just right at the singularity, but near it. Those tidal forces I mentioned get extremely large, and physics almost certainly changes dramatically some distance out from the singular point as various strong-field and quantum effects come into play.

It's possible that the effect of those corrections is to regulate the singularity and spread it out, or remove it entirely. No one knows. One thing to bear in mind is that quantum mechanics doesn't like points. Even "point particles" are really probability clouds, and quantum mechanical effects get very strong near a singularity.

Given that gravity is nothing other than space and time itself, when gravity gets strongly quantum, all hell can break loose...

 

[rjh01]

As I understand it as you get closer to the speed of sound, part of the energy gain is in mass and not speed. This means that you will not go any faster than the speed of light.

Sol is right. A person would feel massive tidal forces inside the space ship as they are very close to the black hole.

One other effect is that from an outsiders point of view, your time will slow down, maybe almost to an halt.

 

[BNRT]

As you approach a singularity, the variation in the gravity field gets stronger and stronger, and the mlld tugging you were feeling will grow stronger and stronger. Before you could actually touch the singularity your body would be torn apart by these forces.

I'd like to add something here. Not because your explanation is lacking, because it isn't, but because it's cool. Also: I may be wrong.

As the force of gravity decreases exponentially with distance (at twice the distance, the force is four times smaller), you experience different forces on, say, your head and your feet. If you fell feet-first into the black hole, your feet would experience a much stronger pull than your head, causing you to stretch.

Near a black hole, these effects are so big that you would be torn apart. This is called (and this is the cool bit spaghettification.

 

[Beth]

One thing to bear in mind is that quantum mechanics doesn't like points. Even "point particles" are really probability clouds, and quantum mechanical effects get very strong near a singularity.

What does this mean? What effects are you talking about here?

Thanks for taking the time to explain this.

 

[uruk]

Gravity does not increase to infinity at the singularity.
The force due to gravity is caused by the mass of the object. For a black hole singularity this mass just happens to be packed into an infinitesimal volume.

So according to Newton, the acceleration is constant. GR may differ.

Little "g" is inversly dependent on the radius of the attracting body. If the radius decreases. little "g" increases.

 

[uruk]

Perhaps check this page out ... farther down the page it says that at 0.35 Schwarzschild radii, relative to observers freely falling radially from rest at infinity, our velocity increases towards the speed of light.

Thanks for the link!. If the gravitational forces increase high enough could the falling body's velocity exceed C?

According to Einstien et. al. There is no limit to the rate at which space/time can contract. Can the singularity contract space/time so that the falling body's velocity exceeds the speed of light?

 

[uruk]

When you're freely falling through a gravitational field you don't feel any force - you float around inside your spaceship like an astronaut. The only exception to that is what are called tidal forces - if the gravity field varies in strength across space, different parts of your body will try to accelerate at different rates, which means you'll feel a tugging as your body holds itself together (this effect is what causes the tides on earth, so these forces are called tidal forces).

As you approach a singularity, the variation in the gravity field gets stronger and stronger, and the mlld tugging you were feeling will grow stronger and stronger. Before you could actually touch the singularity your body would be torn apart by these forces.

As for what happens at the singularity itself, no one knows - it's a place where the laws of general relativity (Einstein's theory of gravity) break down, and it isn't clear what (if anything) should replace them.

As for the horizon - for a large black hole, the horizon is actually completely regular. Tidal forces are weak, and you wouldn't notice anything special as you fell into it.

Thanks. I am aware of effects of crossing the event horizon and "spaghettification". It is really interesting how a black hole pretty much trashes the laws of physics.

What I was wondering is if the gravitational forces could get so high as to cause the velocity of the falling body to exceed the speed of light.

 

[uruk]

As I understand it as you get closer to the speed of light, part of the energy gain is in mass and not speed. This means that you will not go any faster than the speed of light.

~snip~

Would this be the case? Would the gain in your mass also increase the force of attraction between you and the singularity?

I guess Newton would not be sufficient.

What does relativity and quantum mechanics say?

 

[uruk]

Well according to the link posted by trentwray (thanks again) There seems to be a point where an observer will see your velocity exceed C. I don't know if it actually does though.

 

[rjh01]

Would this be the case? Would the gain in your mass also increase the force of attraction between you and the singularity?

I guess Newton would not be sufficient.

What does relativity and quantum mechanics say?

Yes there would be an increase in the forces between you and the black hole as observed by an outside observer. However this would be matched by an increase in mass so acceleration would not go up due to this increase in force. You in the space ship aprroaching the black hole would not observe anything unusual inside the space ship. The stars behind you would look very strange. Red shifted due to your speed and blue shifted due to your location near the black hole. They would also have moved location.

Well according to the link posted by trentwray (thanks again) There seems to be a point where an observer will see your velocity exceed C. I don't know if it actually does though.

However this observer would not be able to see you as you have entered the black hole. Unless the black hole is huge you are also dead due to tidal forces alone. If there is other mass present you probably would be dead from the radiation.

Quantum mechanics would hardly come into play. Exception. If the black hole was very small then it becomes a brown hole. Reason. Quantum mechanics says that you cannot know the exact position of a particle. If the black hole is very small then there is a probability > 0 that a particle that should be inside the black hole is actually outside the black hole and thus can escape. Thus an isolated small black hole will decrease in size. The smaller the black hole the faster this will happen. The end of the brown hole would be spectacular. Thus black and brown holes have a temperature. If this is less than the temperature of the universe then the brown hole needs to find some mass or it is doomed. Any black hole above the temperature of the universe is safe as it absorbs more energy than it loses. Brown holes have never been observed. Observations have been made where the simplest explanation is a black hole. For example in the centre of the galaxy several stars orbit a massive unseen object.




Weird things happen near a black hole, so some of this may be wrong. Sorry for the rant.

 

[sol invictus]

What does this mean? What effects are you talking about here?

Let me try to explain it this way. Imagine an electric field between two plates of metal. The field is there because the plates are charged (one positive and one negative). If the field gets strong enough, the air in between the plates will ionize and a spark will jump from one plate to the other and discharge part of the field. That's an example where the relevant laws of physics describing the region between the plates changed dramatically when the field got very strong. Of course we know what and how and why in that case, but only because we've been able to experiment with air, we know how it ionizes, what it's made of, etc.

That same effect - ionization and discharge - can happen even if there is a perfect vacuum between the plates. The reason is quantum mechanics. Even a perfect vacuum is actually constantly boiling with electron-positron pairs that appear and annihilate. Normally this happens so fast you can't notice it - but if the electric field gets strong enough it will pull those pairs apart and send them to the plates, where they will partially discharge them. So if the field is strong enough even the vacuum ionizes.

What does this have to do with black hole singularities? Well, if the gravity field is strong enough, one should expect effects like this. Pairs of.... something should appear, annihilate, and disappear - but if the field is strong enough, they should have a strong and lasting effect. It's not clear how to "discharge" a singularity, because there is no known negative "charge" in gravity (energies are positive), but there should still be some kind of effect analogous to the vacuum ionizing. That effect, whatever it is, shouldn't be confined to the singular point, it should extend around it in the region where the field is sufficiently strong.

What I was wondering is if the gravitational forces could get so high as to cause the velocity of the falling body to exceed the speed of light.

Measured from infinity, that happens at the horizon (which can be very far from the singularity). That's another way of saying that the horizon is the surface from which light cannot escape. Measured locally by the infalling observer it never happens, although of course at some point she will be torn apart and find it difficult to make accurate measurements.

 

[Helen]

if you accelerate so that you go faster than the speed of light, you black out

 

[ben m]

Measured from infinity, that happens at the horizon (which can be very far from the singularity). That's another way of saying that the horizon is the surface from which light cannot escape. Measured locally by the infalling observer it never happens, although of course at some point she will be torn apart and find it difficult to make accurate measurements.

There's a related point that confused me for a long time. Think about diving headfirst into a large black hole. At some point, your head will be inside the event horizon and your feet will be outside. At this point (assuming nerve signals with speed c) can you still wiggle your toes?

If you can, it sounds like you can get a signal out of the event horizon. You send a signal from your brain (inside) to your toes (outside) and someone on the outside sees your toes wiggle or not.

If you can't, it sounds like there is something special about the horizon---surely you'd notice, in a nearly-local measurement, if your head were suddenly out of causal contact with your feet.

The answer is that you can wiggle your toes; your toes are not out of contact with your head. However, there's a light-travel-time delay between your brain and your toes, and at this stage of your infall your toes are necessarily moving inwards towards the horizon. By the time your toes actually start wiggling, they've passed inside the horizon and no one can see them. So it is both true that (a) local physics doesn't care about the horizon and (b) light-speed signals can't get out of the horizon.