Black Holes and how gravity can overcome light speed?

1. Jan 5, 2009

Boffin

Information
In the book “Black Holes and Time Warps” by Kip Thorne it is mentioned on pg 121 that Einstein didn’t believe that black holes existed so the thinking that black holes can exist didn’t come directly from his writing, thoughts, or how he interpreted his relativity theories. Because Einstein cast doubts on black holes, it seems valid to question or understand why some scientists agree they exist. In the related thread below, most posters discussed whether black holes could exist largely based on formulas. Unfortunately different scientists use different formulas. In this thread I'd like to discuss this question based on rational thinking of basic physics concepts.

Question
Can gravity be so strong that light slows down to nothing or even a negative speed? I thought the general limitations in Relativity were than gravity can become so strong that light slows down to almost nothing but not quite? Aren’t gravity and light speed inversely related, the stronger the gravitational pull, the slower light speed will be in trying to escape the gravitation pull, till the point where gravity is almost infinitely strong and light speed is almost infinitely small?

Black holes and whether General Relativity views light as a ballistic particle?

2. Jan 5, 2009

mgb_phys

Black holes were thought to be just a mathematical possibility by a lot of people - until they were discovered.
Gravity doesn't change the speed of light - it just changes time.
There is no problem slowing light down, a piece of glass does that.
You can get it down to walking pace with the right equipment.

Last edited: Jan 5, 2009
3. Jan 5, 2009

jnorman

light does not slow down, even within a BH. the light cannot escape from the BH because the escape velocity within the event horizon is greater than C.

4. Jan 6, 2009

Boffin

Even scientists often use the concept of absoute light speed in their conceptual explanations. For example I was simply relating the discussion of black holes from p122 from “Black Holes and Time Warps” by Kip Thorne were it says "When a corpuscle of light is lauched from such a star...it will fly upwards at first, then slow down to a halt and fall back to the star's surface". The observer is considered to be a distant one far away from the event calculating the speed theoretically.

The concept of an event horizon is formulae based which can be subject to interpretation of relativity. Therefore saying that light cannot escape from a massive star because of the event horizon is circular thinking if the discussion is determing whether there is even an event horizon.

I'm looking for a concept based explanation to check the interpretation of relativity in relation to massive stars.

Last edited: Jan 6, 2009
5. Jan 6, 2009

JesseM

Keep in mind that even in SR, the coordinate speed of light is only c in inertial coordinate systems, it's perfectly possible to come up with a non-inertial coordinate system such that, for two points on the worldline of a light beam, (change in coordinate position)/(change in coordinate time) is something other than c. In GR there's no way to construct an inertial coordinate system to cover the whole spacetime, but observers in a state of free-fall can still construct "locally inertial" coordinate systems to cover a very small region of space around them for a very small time (technically infinitesimal), in which case the equivalence principle says that in this small neighborhood they will observe the same laws of physics as are seen in an inertial frame in SR (although there are some subtleties in the definition of the equivalence principle, see here if you're interested). So in GR it's always true that free-falling observers whose path intersects with that of a light beam will always locally measure it to be moving at c in the small neighborhood around the crossing-point, even though in some global coordinate system on the curved spacetime, like Schwarzschild coordinates for a black hole, the coordinate speed of light may change at different positions. In particular, a free-falling observer passing the event horizon will locally measure the horizon itself to be moving outward at c (explaining why this observer cannot 'escape' the horizon), so any light trapped on the horizon will still be moving at c as measured by local free-falling observers.

6. Jan 6, 2009

Jonathan Scott

Be careful about what you're saying here.

Many objects have been discovered which are sufficiently massive that according to the standard interpretation of GR they would be black holes.

However, as far as I know, the experimental evidence that they ARE black holes (confirming that interpretation) is very tentative so far. There are some signs that objects with masses around the theoretical borderline between neutron stars and black holes can be classified into two groups according to whether type I X-ray bursts are seen, with the assumption being that the absence of such bursts could be due to an event horizon having formed.

7. Jan 15, 2009

Joe143

a black hole has an infinite curvature thus make all material around it (including light) warp towards its center

8. Jan 16, 2009

JesseM

Here's some papers on the types of evidence that are thought to indicate astrophysical black holes if anyone's interested:

http://arxiv.org/abs/astro-ph/0701228
http://arxiv.org/abs/astro-ph/0310692
http://arxiv.org/abs/astro-ph/0306439
http://arxiv.org/abs/astro-ph/9710352

9. Jan 16, 2009

granpa

the answer to the op is that time supposedly stops at the event horizon. if you believe that.

a normal newtonian object with a normal newtonian gravity field and an escape velocity greater than c could still emit light.

10. Jan 16, 2009

JesseM

Only if you use Schwarzschild coordinates, not in any real physical sense.

11. Jan 16, 2009

granpa

as measured by an observer far from the black hole time stops at the event horizon. thats pretty much what makes a black hole a black hole. otherwise its just a big dense object.

12. Jan 16, 2009

Chewy0087

Okay, was wondering about this, if you're going into a black hole, taking aside the crushing factor, or say that you're in a box that can withstand the pressure until you're extremeley near, am I correct in saying that in your reference frame, your acceleration into the black hole would be so great that time would be dilated to a huge amount?

This would mean that from a reference frame far away I would slow down by that gamma factor? If so, does that mean if time is dilated by 100000000000 for example, relative to them, I would stay alive for another 100000 years or so before dying? :P

Lulz!

13. Jan 16, 2009

stevebd1

Hi Chewy0087. It's not pressure you need to worry about in close proximity to a black hole but tidal forces (or the gravity gradient) which is the measure of the change in gravity $\Delta g=(2Gm/r^3)\Delta r$, anything greater than a change of 10 Earth g over 2 metres and you're in trouble.

Regarding time dilation, for schwarzschild metric (observing from infinity) the time dilation is $dt'=dt\sqrt{1-r_s/r}$ and tends to zero at the event horizon but for the infalling observer who is looking back at the universe he is leaving behind, when looking at Schwarzschild metric in Gullstrand-painleve form (i.e. from the perspective of the infalling observer), the time dilation (or proper time) is virtually the inverse of the Schwarzschild coordinate time dilation and tends to infinity at the event horizon (i.e. the infalling observer will see the universe outside the BH's gravitation field speed up) though there seems to be an argument against the infalling observer supposedly being able to witness the end of the universe- http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html (scroll down)

Steve

Last edited: Jan 16, 2009
14. Jan 16, 2009

Chewy0087

Thanks for the reply Steve, that other link was very helpful aswell, and reguarding the pressure thing, sorry if i wasn't clear, i did word it very badly, but that was what i was referring to :P

Thanks!

15. Jan 17, 2009

Joe143

you wouldnt get crushed by a black hole, you would under go a process called spagettification, and all though you would be long dead the black holes would more rip you apart atom by atom than crush you, all though they both don't seem to appealing. :)

16. Jan 21, 2009

sneh

To be effected by gravity, light would have to have mass, which would then prevent it from travelling at the speed of light in the first place?!

But then, how does light travelling in a vacuum get "sucked backwards" like swimming against a current?

17. Jan 22, 2009

tiny-tim

time dilation

Hi Chewy0087!

If you could safely hover very close to the event horizon, and come away again, yes time dilation means that you would find that everyone else had aged much more than you.

For example, if the event horizon has a radius of 100km, and you hover 10m above it, everyone else will age 100 times more than you.

Of course, your feet will age even slower than your head (if you're "upright"), by about 10%, but even for periods as long as a few years, that shouldn't matter … if you want to eliminate even that, then simply change position occasionally.

18. Jan 22, 2009

granpa

you're forgetting gravitational time dilation.

19. Jan 22, 2009

The Dagda

Well the whole of general and special relativity as well.

Light is bent by gravity because time and space are. If light had mass, it would simply be slightly more affected, given that it would be likely to be as close to zero as damn it, I doubt it would make much difference, or that we could even detect one at least with current technology.

20. Jan 22, 2009

A.T.

Not in General Relativity. You don't need to have mass to be affected by spacetime curvature.

21. Jan 22, 2009

sneh

Fair point.
When we say curve, is that referring to the maths more than literally curved? (My impression is curved space just means it's basically more "bunched up" in physical terms - so like light taking longer to go through glass, it takes longer to travel through denser "bunched up" space.. ?)

22. Jan 22, 2009

A.T.

That is one possible way to envision intrinsic curvature. But it is curved space-time, not just space. See my posts in the other thread:

23. Jan 22, 2009

Jonathan Scott

Re: time dilation

You might try calculating how many "g"s of force you'd be subject to in that case. I've not tried the calculation, but I suspect that it would reduce any earth organism at the very least to a thin film of atoms on the bottom of the spaceship.

24. Jan 22, 2009

sneh

Ah yes, time. Thanks.
I should maybe save further arguments for another thread! (I think only space curves relative time, not time itself)

25. Jan 23, 2009

yuiop

The escape velocity from the surface of the Earth is about 40,000 km/hr.
An object leaving the Earth at 40,000 km/hr would have sufficient velocity to reach infinity.

The escape velocity from the event horizon is c.
An particle leaving the event horizon at c (eg a photon) would have sufficient velocity to reach infinity.

An object leaving the Earth at about 20,000 km/hr km/hr can leave the surface of the Earth and travel a great (but not infinite) distance from the Earth.
An outgoing particle with a velocity of 0.5c can leave the event horizon and travel a great (but not infinite) distance from the black hole.

An object leaving the Earth at about 1 km/hr can leave the surface of the Earth for a short time. (This can be demonstrated by jumping up and down).
An outgoing particle with any positive velocity can leave the event horizon for a short time.

The above statements are made in the Newtonian context and make it clear that escape velocity alone in the Newtonian context, is a useless argument for explaining why particles can not leave a black hole event horizon.

I think mgb is on the right track here.

Sadly Kip is making a very misleading statement here. If a photon is going out perfectly vertically/ radially then it will never come to a stop, turn around and start falling. If he meant that emitted somewhere just above the event horizon at an angle would travel in an arc that may eventually head back towards the black hole then that would be OK, but he should have that clear and a photon outside an event horizon would never come to a stop in a vacuum.

Jonathan is spot on here. There is very little (if any) direct physical experimental evidence for what is supposed to happen exactly at the event horizon or below it. When a pocket of gas falls towards a neutron star it is compressed to such an extent when it hits the surface and that it detonates as a thermo nuclear explosion which can be detected by the radiation given off. Say, for the sake of argument we had a body that was fractionally larger than its Schwarzschild radius, that was tough enough to resist collapse or maybe held intact by some as yet undiscovered Pauli type exclusion principle. Such a body would outwardly look just like a black hole. Radiation from nuclear explosions on the surface of such a body would be red shifted by extreme time dilation into very long wavelength radio waves that would be very difficult to detect, but that would something to look for. It is time dilation that makes black holes look black.

Granpa is right in his second statement. Light would still escape from a body which has an escape velocity greater than light in the Newtonian context. However, I am bit concerned about the use of the word "supposedly" in his first statement. It is the "supposed" time dilation that takes us out of the Newtonian context. Time dilation can explain why we do not see electromagnetic radiation from black holes because of the extreme red shifting of the radiation that makes it difficult to detect. However redshift does not explain why particles can not escape from an event horizon. An electron or neutron leaving the event horizon can not be red shifted in such a way that prevents us detecting it. As granpa mentions and as I argued ealier, a particle can leave a surface and go a long way, even if it is travelling at less than the escape velocity. It is only excluded from going to infinity.

In conclusion, escape velocity and red shift considerations alone, can not explain why particles can not escape an event horizon. It seams the only remaining valid explanation is that we take the radical step of taking the Schwarzschild equations seriously and assuming that time and particles really do slow down near an event horizon.

Red shift and time dilation are two related concepts but they are often confused. Often it is assumed that time does not really slow down near a black hole, but just appears to do so because photons climbing out of a deep gravity well get stretched to longer wavelengths with a lower frequency when detected higher up. To test you understanding, here is a little thought experiment. Imagine a clock is attached to a beacon that emits a pulse of blue light once for every second that passes on the clock. The clock and beacon is lowered towards a black hole. As it gets near the event horizon the pulses of light appear to be red rather than blue becuase to red shift. Now will the observer that stays higher up see the pulses arrive at a rate of one per second or will there be much longer intervals between each pulse? If your answer is that the intervals between pulses is longer than one second, do you see that means the beacon clock really is slowing down relative to your clock? Stretching the wavelength, can not by itself explain the longer interval between pulses. If you accept the lower clock really is running slower and if you agree that an observer lower down will measure the local speed of light to be c (using his slow clock) then the speed of light lower down must be slower relative to the speed of light higher up, even though locally the speed of light appears to be constant everywhere.

It is worth mentioning that it can be shown in Kruskal Szekeres coordinates a radially outgoing photon emitted exactly at the event horizon stays at the event horizon forever (without orbiting). In that sense, if you interpret "not going anywhere" or "staying in the same spatial location" as one meaning of the word “stationary” then a photon can be stationary at the event horizon.

Side note: In relativity the word "stationary" can mean other things. If a brick is placed on the floor so that it is clearly not moving, then most people would say the brick is stationary. In a relativity forum they will say the brick is not stationary because it moving forward in time. (Always read the label).

In relation to the direct question asked in the OP:

.. I would tend to agree with the light slowing down interpretation, as I hope I have made clear in the arguments above, but I should mention that is not the interpretation of modern text books which do not appear to take the view that time slows down in any real way near a black hole. There is also the view expressed by someone in another thread, that even though a photon may be stopped at the event horizon, to an infalling observer (who considers himself as stationary in Kruskal-Szekeres coordinates) the trapped photon and the event horizon it is trapped in, are coming towards the infalling observer at the speed of light, so the infalling observer sees the stationary photon as moving at c.