PDA

View Full Version : What is the reason light can't escape from a black hole?



BetaDust
2018-Jan-19, 11:13 AM
If there is nothing that can go faster than light, what is preventing light from escaping the event horison of a black hole?
Is it the the gravitational force of the singularity?
And if so, does this mean the gravity of the black hole exeeds the speed of light?

-- Dennis

Lazer
2018-Jan-19, 02:10 PM
No nothing can travel faster than light.

Every physical body has an escape velocity (https://en.wikipedia.org/wiki/Escape_velocity).
When this velocity is >= the speed of light it is impossible to escape, even for light.
This is a black hole.

In reality gravity is curved space, and in a black hole space has curved into itself.
Light will always follow the space curvature.

A black hole is not necessarily small, the more the mass the less density is required.
This means if the mass is large enough the "gravity force" may be small.

The universe may be a big black hole.

Cheers
L-zr

Strange
2018-Jan-19, 02:34 PM
As Lazer says, it is because of the extreme curvature of space-time. Once you pass the event horizon there are no paths that lead away from the singularity. In fact, the radial dimension and the time dimension "swap places" when you pass the event horizon, and so the singularity is no longer (physically) ahead of you, but is in your future. That is why you can't avoid it.


Every physical body has an escape velocity (https://en.wikipedia.org/wiki/Escape_velocity).
When this velocity is >= the speed of light it is impossible to escape, even for light.

The trouble with this (common) explanation is that the escape velocity doesn't stop you leaving. For example, you can throw a ball or launch a rocket from Earth at less than escape velocity. It will eventually fall back, though. But you can never leave a black hole, even temporarily. (I'm sure you know this, just thought it was worth clarifying.)

BetaDust
2018-Jan-20, 02:00 PM
No nothing can travel faster than light.

Every physical body has an escape velocity (https://en.wikipedia.org/wiki/Escape_velocity).
When this velocity is >= the speed of light it is impossible to escape, even for light.
This is a black hole.



You say "When this velosity is >= the speed of light", does this mean the gravitational pull of this object exeeds the speed of light?
So can gravitational pull exeed the speed of light? How is this possible if nothing can go faster than c?

-- Dennis

Strange
2018-Jan-20, 03:05 PM
You say "When this velosity is >= the speed of light", does this mean the gravitational pull of this object exeeds the speed of light?
So can gravitational pull exeed the speed of light? How is this possible if nothing can go faster than c?

-- Dennis

Gravitational "pull" cannot be equated to a speed. In the simplest case it is a force, given by Newton's law: proportional to the product of the masses and inversely proportional to the square of the distance. As a result the force on an object is greater if it has more mass. But the force needed to accelerate something increases with its mass (Newton again). As a result, the acceleration of objects of any mass will be the same in a given gravitational field. Hence gravity can be described in terms of acceleration: the gravity on the surface of the Earth is often described as g = 9.8 m/s2.

BetaDust
2018-Jan-20, 04:05 PM
Thank you Strange!

I think i'm lost.

In the first quote you say gravitational pull cannot be equated to a speed:


Gravitational "pull" cannot be equated to a speed.

But in this quote you give a speed for the gravitational pull of the earth. e.g. 9.8 m/s2:


Hence gravity can be described in terms of acceleration: the gravity on the surface of the Earth is often described as g = 9.8 m/s2.


I'm very sorry for not understanding what you just explained to me.
Please bear with me, i'm just trying to get a better understanding of this wonderfull world around me.

-- Dennis

grapes
2018-Jan-20, 04:08 PM
You say "When this velosity is >= the speed of light", does this mean the gravitational pull of this object exeeds the speed of light?
So can gravitational pull exeed the speed of light? How is this possible if nothing can go faster than c?

Gravitational pull is not a speed/velocity, it is a force. The result of such a great force is that space is warped, and there is no path in spacetime that leaves the black hole

Strange
2018-Jan-20, 04:17 PM
In the first quote you say gravitational pull cannot be equated to a speed:

But in this quote you give a speed for the gravitational pull of the earth. e.g. 9.8 m/s2:

That is an acceleration not a speed.

The force of gravity causes a body to accelerate - and so the speed will depend on how long it accelerates for. I guess this will usually be limited by hitting the floor! (In which case, the [final] speed is determined by the force of gravity and the height you fall from.)

skymapper
2018-Jan-20, 04:28 PM
But in this quote you give a speed for the gravitational pull of the earth. e.g. 9.8 m/s2:

That's not a speed, it's an acceleration.

Drop something near the surface of the earth and let it fall. Ignoring air resistance, how fast should it be moving?

After 0 seconds, it is falling at 0 m/s (metres/second)
After 1 second, it is falling at 9.8 m/s (metres/second)
After 2 seconds, it is falling at 19.6 m/s (metres/second)
After 3 seconds, it is falling at 29.4 m/s (metres/second)
After 4 seconds, it is falling at 39.2 m/s (metres/second)
After 5 seconds, it is falling at 49.0 m/s (metres/second)

How is the speed of this falling object changing? It is increasing by 9.8 m/s each second. So the acceleration is 9.8 metres per second, per second. Often written 9.8 m/s2.

Strange
2018-Jan-22, 09:16 AM
...

Thanks for explaining that - and so clearly. It is too easy to assume that people are familiar with the basics when, for any number of reasons, they might not be.

BetaDust
2018-Jan-22, 08:22 PM
Gravitational pull is not a speed/velocity, it is a force. The result of such a great force is that space is warped, and there is no path in spacetime that leaves the black hole

Thanks grapes and also Strange, Laser and Skymapper.

So gravitational pull is a force, e.g. m/s2, an acceleration. But how does that acceleration exeed the speed of light?

I'm sorry if my questions don't make any sense, it is hard to get my head around it.

Thanks again,

-- Dennis

Shaula
2018-Jan-22, 09:36 PM
So gravitational pull is a force, e.g. m/s2, an acceleration. But how does that acceleration exeed the speed of light?
It doesn't - you are not comparing like with like here. Saying an acceleration exceeds the speed of light is like saying a kilogram is bigger than a degree Celsius - they are different units and relate to different physical quantities.

Can you explain what you think is moving faster than light? In GR gravity is modelled as curvature of spacetime, it doesn't 'move' (for a static solution such as a large mass - changes in a gravitational field do propagate but they are not really relevant to this question). It is more like a dip in spacetime you have to expend energy to climb out of (just like going uphill). If we roll a marble uphill and it doesn't have enough energy/speed to roll all the way up the slope we don't say that the hill has to be moving or that the speed of hill exceeds the speed of marble.

Jeff Root
2018-Jan-22, 09:47 PM
An essential part of the answer to your question is the fact that
all speeds are relative. No exceptions.

That is very hard to understand given the additional fact that the
speed of light in vacuum is the same for all observers. A huge
number of posts in this forum have been devoted to explaining
this strange combination of facts. Many people are so perplexed
by what seems to them to be a contradiction between those two
facts that they make up endlessly convoluted arguments against
one or the other. But both have long been clearly established by
observation.

Gravity is so strong just outside the event horizon of a black hole
that everything falls in except for light which is heading directly
away from the black hole. An observer falling into a black hole
will see light that is coming from just above the event horizon
pass him at the speed of light.

Gravity is so strong inside the event horizon that everything falls
in, including light which is heading directly away from the black
hole. An observer falling into the black hole will see light emitted
inside the black hole pass him at the speed of light. The gravity
is so strong that light heading directly away from the center of
the black hole is actually falling toward the center. But it moves
upward at the speed of light relative to the falling observer.

Interesting, isn't it?

-- Jeff, in Minneapolis

Jeff Root
2018-Jan-22, 10:18 PM
Since Shaula mentioned the "dip in spacetime" analogy, I'll point
out that it is humorously ironic that we use gravity as an analogy
to explain how gravity works.

We can do that because what gravity does is very familiar to
everyone, but how it does that is not obvious and needs to be
explained. We explain it with an analogy involving the familiar
action of gravity.

-- Jeff, in Minneapolis

Strange
2018-Jan-22, 10:23 PM
So gravitational pull is a force, e.g. m/s2, an acceleration. But how does that acceleration exeed the speed of light?

Firstly, this is all a bit of a distraction from the original question you asked about why light can't escape. The answer to that has nothing to do with speeds or acceleration. However, now we are talking about the relation between gravity and acceleration ...

Gravity will cause a force on objects. That force will be larger for objects with more mass. The force will cause the objects to accelerate as they fall to the ground. (This is Newton's second law of motion: F=ma https://www.grc.nasa.gov/www/k-12/airplane/newton.html)

Because these falling objects are accelerating, they will gain more speed over time. So the higher they fall from, the faster they will be going when they hit the ground. (The math gets a bit more complicated here, because the force of gravity decreases with height as well. But we can ignore that detail for the moment.)

If they fall from a large enough distance (strictly speaking from an infinite distance) then when they hit the ground they will be moving at the escape velocity of the planet (the speed something would have to be doing in order to never fall back).

It so happens that the escape velocity at the event horizon of a black hole is the speed of light (even though this is NOT the answer to your original question). This also means that if something free falls towards a black hole (from far enough away) then it will just reach the speed of light as it passes through the event horizon. But it will not exceed the speed of light.

Hope that helps!

Jeff Root
2018-Jan-23, 12:04 AM
Because these falling objects are accelerating, they will gain more
speed over time. So the higher they fall from, the faster they will be
going when they hit the ground.

If they fall from a large enough distance (strictly speaking from an
infinite distance) then when they hit the ground they will be moving
at the escape velocity of the planet (the speed something would
have to be doing in order to never fall back).

It so happens that the escape velocity at the event horizon of a
black hole is the speed of light.
Of course, when you say "It so happens ..." you aren't implying that
it is a coincidence. The event horizon is an event horizon because
the escape speed there is the speed of light.



This also means that if something free falls towards a black hole
(from far enough away) then it will just reach the speed of light as
it passes through the event horizon. But it will not exceed the
speed of light.
It seems incredible, but a falling object just reaches the speed of
light as it passes through the event horizon even if it started falling
from a very short distance away. Even an inch.

But as I said in a post above, speed is always relative. The speed
of an object reaching the speed of light as it passes through the
event horizon is relative to a distant observer who is not moving
relative to the black hole. It is also relative to the event horizon
itself, although no observer could be located there to measure
the relative speed.

Also, the object does not stop accelerating at the event horizon.
Its speed away from a distant observer continues to increase.
But no distant observer can ever see anything that passes through
the event horizon. That faster-than-light relative speed is just a
mathematical fact, not something that can be observed.

-- Jeff, in Minneapolis

Strange
2018-Jan-23, 02:46 PM
Of course, when you say "It so happens ..." you aren't implying that
it is a coincidence. The event horizon is an event horizon because
the escape speed there is the speed of light.

While it is not a coincidence, the event horizon is an event horizon because of the curvature of space time, not because of escape velocity.

If it were because of the escape velocity, then it wouldn't be an event horizon at all, because light and even "things" could escape the event horizon (temporarily).

Jeff Root
2018-Jan-23, 05:52 PM
The event horizon is where the escape speed is the speed of light.
It is at that location where it becomes impossible for anything to
escape, even including light. The event horizon is defined by that
fact. The curvature of spacetime is of course what causes the
escape speed to have such a value.

-- Jeff, in Minneapolis

grant hutchison
2018-Jan-23, 06:16 PM
While it is not a coincidence, the event horizon is an event horizon because of the curvature of space time, not because of escape velocity.

If it were because of the escape velocity, then it wouldn't be an event horizon at all, because light and even "things" could escape the event horizon (temporarily).Each are both. The nature of spacetime at the event horizon leads to the inability of light to escape from that particular location. The Newtonian idea of escape velocity doesn't apply in these extreme situations, in the sense of stuff being able to rise above the launch point before falling back again if they have less than the necessary velocity of escape. Outside the event horizon, outwardly directed light signals can propagate outwards. Inside the event horizon, outwardly directed light signals are drawn towards the singularity. At the event horizon, these outwardly directed photons stay constantly at the same radial Schwarzschild coordinate.

I've been hesitating to introduce the Gullstrand-Painlevé metric into this thread, because it can make a complicated picture even more complicated, but it's a useful way of imagining what's going on. In Gullstrand-Painlevé coordinates, space is flowing inwards continuously, and the flow rate rises to the speed of light just as it crosses the event horizon. An infalling observer is at rest in the Gullstrand-Painlevé coordinates, and outward directed photons move like fish swimming against the flow of a river, which means a photon emitted at the moment of crossing the event horizon simply sits at the Schwarzschild radius, propagating outwards at the same speed as space flows inwards.

Grant Hutchison

BetaDust
2018-Jan-23, 07:28 PM
So in the case of a black black hole, does the gravitational force of the singularity is so big even light can't escape the event horison?

-- Dennis

grant hutchison
2018-Jan-23, 07:38 PM
So in the case of a black black hole, does the gravitational force of the singularity is so big even light can't escape the event horison?In the standard model of a non-accreting black hole, light cannot escape the event horizon. Photons emitted at or below the event horizon cannot reach any point beyond the event horizon.
That's why it's called an event horizon - anywhere outside the event horizon, we cannot become aware of events taking place anywhere inside the event horizon, because signals from that region cannot reach us.

Grant Hutchison

BetaDust
2018-Jan-23, 08:32 PM
In the standard model of a non-accreting black hole, light cannot escape the event horizon. Photons emitted at or below the event horizon cannot reach any point beyond the event horizon.


What is preventing the photons from escaping? Is it the gravitational force exeeding c?

I'm sorry asking this many questions, but it's difficould for me to translate al what is posted.
And than try to understand it.

So Thanks for your aswers grand, Jeff and Strange.

-- Dennis

BetaDust
2018-Jan-23, 08:46 PM
What it is that i don't understand:

If photons are the absolute fastest things that exsist,
How can there be anything or any force holding them back?

-- Dennis

George
2018-Jan-23, 09:42 PM
If photons are the absolute fastest things that exsist,
How can there be anything or any force holding them back? I would think framing this in terms of escape velocity might help, though there is a bigger story than just escape velocity...

You need a velocity of a little over 11 km/sec to sling-shot an object completly away from Earth, ignoring air resistance. If the mass of the Earth increased, or the Earth shrunk, the gravity at the surface would increase and thus increase the escape velocity. Schwarschild, a year after Einstein introduced General Relativity, solved the equations for the condition where the escape velocity would be that of light. The imaginary sphere at that radius is the Event Horizon. From that point inward, the speed of an object must be faster than light to escape, which is, of course, faster than the speed of light.

Another analogy, if I understand it, is to model all this by having spacetime flow into the blackhole, so it would be like a Barbel fish trying to swim up a waterfall that is falling faster than the speed it can swim.

grant hutchison
2018-Jan-23, 09:45 PM
What it is that i don't understand:

If photons are the absolute fastest things that exsist,
How can there be anything or any force holding them back?

Well, you're maybe aware that General Relativity allows space to expand faster than light - distant galaxies are being carried away from us faster than light by the expansion of the Universe. The mathematics tells us that all these objects are locally at rest, but the expansion of space is moving them apart. Photons emitted by these distant galaxies, even though they are directed towards us, are carried away from us by the expansion of space.

So, too, when we look at the space around a black hole using the Gullstrand-Painlevé metric, the maths tells us that space is flowing into the black hole. At the event horizon it is flowing at the speed of light. Within the event horizon, it is moving faster than light. Anything at rest in the Gullstrand-Painlevé metric is actually falling into the black hole. A photon emitted outwards at the event horizon will move outwards at the speed of light, but will also be carried inwards at the speed of light. It'll be stuck at the event horizon, like a man running up a down escalator.

You can find more detail at Andrew Hamilton's excellent site (http://jila.colorado.edu/~ajsh/insidebh/waterfall.html) - he uses the analogy of a fish going up a waterfall.

Grant Hutchison

George
2018-Jan-23, 10:15 PM
You can find more detail at Andrew Hamilton's excellent site (http://jila.colorado.edu/~ajsh/insidebh/waterfall.html) - he uses the analogy of a fish going up a waterfall.
[FWIW, my fish analogy wasn't an act of Google fu. ;)]

BetaDust
2018-Jan-23, 10:55 PM
That link was really helpfull! Thanks.

From the link:


any light emitted within the horizon is dragged inward, even if the light is pointed directly outward.


A black hole is a place where space is falling faster than light .

So it is space itself doing this, the light is just getting caught into this?

-- Dennis

Strange
2018-Jan-23, 11:07 PM
What it is that i don't understand:

If photons are the absolute fastest things that exsist,
How can there be anything or any force holding them back?

You need to get away from the Newtonian view of gravity as a force (which is why the "escape velocity" argument doesn't really work).

Gravity is caused by the curvature of space and time. (That is quite a difficult concept to get your head round anyway.) And when you get to the event horizon then the curvature of space and time becomes so great that there are no longer any routes that will take you out of the black hole; they are all so extremely curved, they just lead you back in towards the centre of the black hole. (That is not completely accurate, but it might give you an idea.)

Grant mentioned the Gullstrand-Painlevé metric. This might be quite useful as it does, in a way, relate gravity to speed. There is quite a graphic explanation of it here: http://jila.colorado.edu/~ajsh/insidebh/waterfall.html

I would caution, though, that this description of space flowing in to the black hole is just an analogy. Space isn't "stuff" and so it's not like liquid flowing down the drain.

p.s. just seen that Grant has posted the same link... (and his works!)

grant hutchison
2018-Jan-24, 01:05 AM
So it is space itself doing this, the light is just getting caught into this?You could say that.
"Space itself" is a slippery concept, though, and any of these analogies only serve to illustrate a particular aspect of the mathematical theory of General Relativity.

Grant Hutchison

Jeff Root
2018-Jan-24, 05:27 AM
You need to get away from the Newtonian view of gravity as a force
(which is why the "escape velocity" argument doesn't really work).
I expect you're right that the escape velocity explanation has
problems, but I'm not clear on what you think those problems
are, or whether they are fatal to the explanation.

Massless things behave very differently from massive things,
and that difference is not described by Newtonian mechanics.
Is that the problem you see?



Gravity is caused by the curvature of space and time.
We can also say that gravity *is* the curvature of space and time
(spacetime), or say that gravity is the main effect of the curvature
of spacetime. The curvature, in turn, is caused by the presence
of matter, which has mass, energy, and pressure. Without matter
there can be no mass, energy, or pressure, thus no curvature and
no gravity. I think it is further true that without matter, there can
be no spacetime. Spacetime without matter can be described
mathematically, but it is very boring and -- I think -- physically
impossible.



... Gullstrand-Painlevé metric...
I would caution, though, that this description of space flowing in to
the black hole is just an analogy. Space isn't "stuff" and so it's not
like liquid flowing down the drain.
I agree that space isn't "stuff" and doesn't behave quite like flowing
liquid, but there *are* similarities. It isn't clear to me that it is just
an analogy. The "picture" (as Ken likes to say) of spacetime flowing
into a black hole isn't required to describe or understand what is
happening, but when it comes to the cosmic expansion, I don't see
how it can be avoided. And I don't see any reason to say that it is a
flow of spacetime in one case but not in the other.

-- Jeff, in Minneapolis

Strange
2018-Jan-24, 09:32 AM
I expect you're right that the escape velocity explanation has problems, but I'm not clear on what you think those problems are, or whether they are fatal to the explanation.

Well, the main one is that you can leave the surface of a body at less than escape velocity. So the fact that escape velocity is the speed of light would not stop you leaving.


Spacetime without matter can be described mathematically, but it is very boring

My understanding is that vacuum or zero-energy models have been studied and provided some insights into GR. So in that sense they are not boring.


I agree that space isn't "stuff" and doesn't behave quite like flowing liquid, but there *are* similarities.

Of course, That is why it is a useful analogy.


It isn't clear to me that it is just an analogy.

Perhaps it would be more accurate to say that the coordinate system flows. But then that isn't such an easy thing to picture; which is why we use analogies.

grant hutchison
2018-Jan-24, 09:45 AM
I agree that space isn't "stuff" and doesn't behave quite like flowing
liquid, but there *are* similarities. It isn't clear to me that it is just
an analogy. The "picture" (as Ken likes to say) of spacetime flowing
into a black hole isn't required to describe or understand what is
happening, but when it comes to the cosmic expansion, I don't see
how it can be avoided. And I don't see any reason to say that it is a
flow of spacetime in one case but not in the other.It's space that "flows" in the black hole analogy and "expands" in the Universe analogy, not spacetime. These processes have to take place in time, not of time.
And there's the reason not to take the analogy too seriously. Because different observers parse spacetime into different components of space and time, the thing that "flows" relative to the thing that times the flow is different for different observers. In the black hole case, there are metrics in which the flow occurs and metrics in which it does not. It doesn't take much reasoning from the flow analogy to go badly wrong under these circumstances.

Grant Hutchison

Strange
2018-Jan-24, 10:32 AM
Grant, in the Gullstrand-Painlevé metric is the speed of the flow always equal to the escape velocity (e.g. if it is applied to the Earth)?

And is there an equivalent metric for rotating black holes?

grant hutchison
2018-Jan-24, 12:10 PM
Grant, in the Gullstrand-Painlevé metric is the speed of the flow always equal to the escape velocity (e.g. if it is applied to the Earth)?
I think this is answered on Andrew Hamilton's web page (http://jila.colorado.edu/~ajsh/insidebh/waterfall.html).
Physically, the Gullstrand-Painlevé metric describes space falling into the Schwarzschild black hole at the Newtonian escape velocity. Outside the horizon, the infall velocity is less than the speed of light. At the horizon, the velocity equals the speed of light. And inside the horizon, the velocity exceeds the speed of light. Technically, the Gullstrand-Painlevé metric encodes not only a metric, but also a complete orthonormal tetrad, a set of four locally inertial axes at each point of the spacetime. The Gullstrand-Painlevé tetrad free-falls through the coordinates at the Newtonian escape velocity.So important to point out that this metric applies to an observer free-falling from infinity, and can't be applied to someone standing on the surface of the Earth.


And is there an equivalent metric for rotating black holes?Farther down the page, Hamilton seems to imply that the Kerr metric does this job.

Grant Hutchison

Strange
2018-Jan-24, 12:59 PM
Ah, thanks. I missed those bits.