Value of g near a black hole (re-visited)

pervect

It is impossible for matter to travel at the speed of light. You say that as if someone said otherwise??

Naty1

Can you explain what you think is 'hype'?

The horizon is a very interesting boundary.....and if fully understood might reveal some underlying relationships difficult or impossible to otherwise detect. Not so long ago, black holes and horizons here virtually 'science fiction'...Einstein, for eample, did not initially believe they could exist.

Here are two descriptions that reveal some of that 'character' of horizons:


Kip Thorne says (Lecture in 1993 Warping Spacetime, at Stephan Hawking's 60th birthday celebration, Cambridge, England,)

and this one from Mitchell Porter [ a forum paritcipant]:

questionpost

How come I don't see this "infinite warping and time flowing backwards" when I look at a computer model that just shows a finitely deep well? It doesn't even make sense that time would stop, because then how would anything ever reach the singularity to add to its mass?

pervect

Time isn't absolute. If you'll recall from special relativity (and if you don't recall it from special relativity, it's really helpful to learn some before trying to tackle General Relativity), it's possible for someone in frame A to conclude that frame B's clock's run slow, while someone in frame B concludes that A's clocks run slow. This is a consequence of the relativity of simultaneity.

It may also be helpful to note that event horizons, very much like the event horizons of a black hole, form in special relativity whenever an observer accelerates - the so called Rindler horizion. A consideration of the Rindler horizon can be very helpful in understanding the event horizon of a black hole.

There's some discussion of this at http://www.gregegan.net/SCIENCE/Rind...erHorizon.html, using basic calculus (no tensors).

The quick explanation is that a clock stopping is not an absolute fact, but some observers might see a clock as stopped, and other observers won't.

questionpost

Yeah, some people "would" see time as being stopped *If it was possible* to do things like travel at the speed of light or infinitely warp the fabric of space. The event horizon for a black hole seems like just an extension of Rindler logic, but as with other examples in relativity such as with relative velocity, you can't use the "Va +Vb= total velocity" for two objects moving away from each other near the speed of light, you need a completely different and more accurate equation that asymtotes at c which is specifically helpful for extremes such as when you have two objects approaching the speed of light.
However, I have yet to see any experiment where we actually see the clocks completely stopped or moving backwards as a result of the somehow infinite distortion of the fabric of space. The event horizon isn't even a physical boundary, it's just the given distance from the singularity at which you can't escape unless you accelerate faster than light. There's still infinitessimal amounts of escape velocities higher than the speed of light inside the event horizon, and there's an infinitessemal escape velocities less than the speed of light outside of it, for some reason people just happen to focus on the escape velocity that is exactly c.
This reminds me of when people said time traveling to the past or distant future was possible just because they saw electrons jumping from one point to another without appearing in the intervening space, and it turns out it had nothing to do with the speed of light or even time, it's completely different math and completely different things that are happening.

PAllen

I dispute the meaning of "escape velocity" inside the horizon. For one thing, you have to be able to escape for this to have meaning. Any tiny region inside the horizon looks just like a tiny region of interstellar space. Matter can only only travel on timelike paths, light on null paths, thus there is no escape path at all, period.

Another way of looking at this is that escape velocity is outside the horizon is defined relative to static observers (you can never talk about any velocity without specifying what it is relative to). Well, there are no static observers at or inside the horizon.

So forget this nonsense about 'escape velocity' greater than c.

questionpost

Well there's the problem right there, because contrary to what your saying what reality is, which is based on improper extrapolations of math in the same way as how I was saying, I can punch in an equation for escape velocity based on gravity and find it eventually gets to a point where it's larger than light. Even if it's physically impossible to have that relative point, I can use my calculator and still find a greater escape velocity than light the same way that you can punch in an equation and calculate that the fabric of space is "infinitely" warped or that time moves backwards.

PAllen

You will never see an experiment showing clocks moving backwards if GR is true because there is no such prediction in GR (even on a closed time like curve you don't see a clock moving backwards). As for completely stopped, you only see this as limiting condition whether you are watching a black hole from a distance or watching ever more accelerated particles. We certainly see particles whose decay clocks are slowed by a factor a millions or more. Damn close to being stopped.

PAllen

We're discussing GR in this forum. If you want to discuss some other theory, go somewhere else. If you think GR predicts 'greater than c' escape velocity, you better explain what you mean in GR terms. You would be wrong, but we can discuss misunderstandings of GR here.

questionpost

GR says as you distort the fabric of space more, the slower time moves in that distortion relative to an outside observer right? Well if we can't have an outside observer, how do we actually know that what your saying is true about the fabric of space with a black hole especially if I can use an equation to "prove" the existence of greater escape velocities than light?
If time wasn't flowing relative to an observer inside the black hole, then the couldn't possibly see that the singularity is coming closer to them because they couldn't be traveling distance over time since for them time has stopped right? So they would never reach the singularity, according to the math alone...
They would have to travel distance over time in order to reach the singularity, because the singularity is x distance away from the observer, unless the event horizon somehow is the singularity. I can even read books that say something like "oh yeah, it would take a week or so for an in-falling person to reach the very center of a massive black hole".
It doesn't even make sense when people say "We would see that light get's frozen at the event horizon" because we wouldn't ever be able to observe if the photons are trapped at the event horizon because then they wouldn't be able to make it to our eyes if they were frozen.

PAllen

I'm not saying we can know or observe what happens inside an event horizon. Therefore, it is meaningless to discuss what 'really' happens inside, and is outside the scope of this forum. However, we can discuss what GR, as a theory, predicts happens inside, for different types of black holes.

GR predicts time flow perfectly normally for an observer crossing the horizon, and allow calculation of exactly how much time (quite short) before they reach the singularity. An outside observer sees them slow down, darken, and fairly quickly become invisible.

I repeat, if you want to talk about something other than GR, you need to do that in a different forum. If you dispute what GR predicts, please explain where everyone else is mis-interpreting the math of GR.

questionpost

Some of what was said GR predicts doesn't seem to coincide with what other aspects predict...
How does time flow so perfectly normal if the fabric of space is "infinitely" warped and matter would follow that warp or if time flows backwards or "downwards"? If time went the other way, wouldn't you travel further away from the singularity since matter will follow the path of the fabric of space-time only to perpetually approach the event horizon to try and cross into the rest of the universe and thus not make it to the singularity? Or might you even be "stuck" at the event horizon because time flowing the other way would mean your exiting the black hole yet outside the black hole time is flowing forwards?
There should just be a few wierd things that might happen, but instead there's all sorts of different things that contradict themselves.
I mean, we can predict what would happen if matter went at the speed of light yet have an equation right next to it that says matter cannot travel at the speed of light because it's speed asymtotes at C.

PAllen

Warped is a poetic term, not physics or mathematics. The accurate statement is: there is a curvature singularity inside a black hole horizon. There is no singular or extreme local behavior at the horizon of a sufficiently large black hole. Time flowing backwards or downwards is simply nonsense, not part of GR at all. Where are you getting this from? Probably you are reading nonsense and believing it is an accurate portrayal of GR.

questionpost

Not to single them out, but stuff like this as well as the books of people like Michio Kaku and Brian Green are confusing or conflicting.




I get that time slows relative to an observer as distortion increases, but just as with traveling at the speed of light, it seems like that should only happen asymtotically. Stopping? From an outside observer's calculations, the in-falling object should never reach the singularity and thus the black hole would never gain mass relative to the outside observer even though the in-falling object would hit the singularity and add to it's mass? And time flowing towards the future infinitely or what?
The gravitational or electric field of a black hole is suppose to be time-frame independent, so how would you measure a change in it originating from the singularity once mass added to it especially if you can't even observer an object crossing the event horizon?

Nabeshin

Correct. More specifically, the observer will never be seen to cross the event horizon.

False, see my post here: http://physicsforums.com/showpost.ph...2&postcount=10

PeterDonis

The infalling object doesn't have to reach the singularity to increase the black hole's mass. Actually, it doesn't even have to reach the horizon, strictly speaking. If you are orbiting the black hole at some radial coordinate r outside the horizon, you will see the effective mass of the black hole increase as soon as the infalling object falls inside your radius. (Strictly speaking, this is what you will see if the infalling object falls right by you on its way in; i.e., if its angular coordinates theta, phi are exactly the same as yours. If it falls at some other theta, phi, it may take time for the effect to propagate to you before you actually see an increase in mass.)

This is true because the gravity of the black hole (meaning, the perceived effects of gravity outside the horizon) doesn't actually come from "inside" the hole (meaning from inside the horizon). It comes from the past, from the collapsing matter that originally formed the hole. See this post (or the thread it is part of) for more:

http://physicsforums.com/showpost.ph...8&postcount=24

An object of non-negligible mass falling into the hole works similarly; it contributes to the "mass" that is measured at a particular event in the exterior of the hole if the infalling object is anywhere in the past light cone of that event.

It is true that the "black hole is frame-independent" in the sense that the presence of an event horizon in the spacetime is frame-independent; if it's there for any observer, it's there for all observers. But in order to say that the "field" is frame-independent, you must first define what you mean by "the field". There are aspects of it that are (in an appropriate sense) frame-independent, but there are others that are not. (I'm mainly talking about the gravitational field here.)

The spacetime that the hole is in is only time independent if the black hole never has anything fall into it. If something of non-negligible mass falls into the hole, the hole changes; the spacetime the hole is in is no longer time-dependent.

PAllen

None of these are contradictory, though Thorne is at least misleading in an attempt a drama.

Let's take them one at a time:

A clock approaching the horizon appears to approach stopping ... from the point of view of an observer further away. That is all, nothing more. This says nothing about the behavior of the clock from its own point of view.

"There is no such thing as a stationary clock at the event horizon." Here, you are rather naturally confused by ambiguity in English language. Pervect is here referring to stationary in the sense of motionless relative to distant observers, not rate of time flow on a clock. The two senses of stationary juxtaposed this way lead to false perception of contradiction. Sorry about that. English is a .... <forum rules> sometimes.

Pervect's statement about the horizon moving at c past any infaller is simply true. To the infaller it simply appears as the light of prior infallers reaching them. Thus the moment they cross the horizon is the moment they can see all prior infallers. I don't see the tension with any other statements.

Now for Thorne. Unambiguously true is that the singularity is a point in time along an infaller's world line, not a spatial point. The infaller sees all prior infallers and all of the outside universe 'normally - except for frequency shift and lensing distortions' until they reach the singularity. They never see anyone else reach the singularity because they reach it (in time) before any light from someone else reaching it can get to them. Specifically, the last they see of any prior infaller is from some moments before that infaller reached the singularity.

Thorne's comments about "a direction you would have thought was spatial" and a "downwards direction" are misguided. The only one expecting this would be someone who interpreted coordinates according the letter used to name them rather than their physical characteristics. In standard Schwarzschild coordinates, the coordinate called 'r' is spacelike outside the horizon and timelike inside the horizon. This means nothing except that 'r' is a bad label for the coordinate inside the horizon. If you instead use the local Fermi-Normal coordinates of a infaller, all of this nonsense disappears.