How do black holes grow?

PAllen

False. It is a place where this happens in one coordinate system that is ill fitted to this region. In other coordinates this does not happen. On the other hand, even these coordinates you can show that curvature is finite at the EH.
False again. There are interior and exterior SC coordinates. Using these, holding theta,phi constant, you compute proper time along a radial free fall geodesic from both sides. You get finite time to reach the EH, in the limit; you get finite time to the singularity in the continuation. In other coordinates, you don't even need to do this - it is just one continuous line.
The infinities at the EH are a coordinate artifact. This is routine differential geometry. Unlike QFT which has pure math problems with its foundations, differential geometry is completely rigorous, and GR is expressed in terms of differential geometry.
That is probably true, but doesn't justify making false statements about the classical theory.
That's also fine.

thehangedman

Yes, it happens in one particular coordinate system. I never said it happened in all coordinate systems. This particular coordinate system is used, however, to show what the event horizon is and to do an easy calculation for it. It is HARDLY just an "artifact".

Fair enough, but I think it is important to people trying to learn this stuff to realize that what you are doing is a bit of a mathematical trick. The trick is entirely valid, and the difficulty comes in peoples minds when they attempt to reconcile the meaning behind the math. A coordinate system is just a mathematical choice, and in the end people need to think about these things in a more geometrical way, but certain coordinate systems are tied to reference frames, and so have a physical meaning. As such, per the original poster's question, there are really only two coordinate systems we can use that tie directly to the experience being asked about: the one that follows the falling object into the BH, and the one of an external observer (certain assumptions made for simplicity).

I think we all agree (as we should, since it's a known) that the object falling into the BH, from it's own reference frame, just falls straight in with a finite time. We also all know that the light (or, more accurately, information) emitted from the falling object to the external observer would never contain anything that shows it actually cross the EH. That is, the external observer never "sees" the object cross the EH. The effects of gravity still increase, but really that has little to do with the BH swallowing anything.

Calling something that is highly physically important and the center of the whole issue here a simple "artifact" if ridiculous and misleading. Just because you can make a coordinate shift to push out the "crinkle" doesn't mean it isn't there. You've just hidden it inside your coordinate map. To point, the observer falling into the BH might not experience a "horizon" directly but WILL see some weird effects from the outside world as they close in on that line. The line is still there, it's still relevant, it just expresses itself differently because we are in a different coordinate system.

Infinities are stubborn little things. They can be moved around, twisted and manipulated, but rarely can you ever make them go away.

PAllen

I believe this is mathematically and conceptually invalid. The event horizon is not an artifact. However, there are no geometric discontinuities there, of any kind. All infinities there (rather than at the true singularity) are pure coordinate artifacts. Infinities from coordinate artifacts can occur anywhere. It just happens the for one coordinate system, coordinate infinities happen at the horizon.

Example: Consider a plane, in x,y cartesian coordinates with Euclidean metric. I transform to new coordinates u=xy, v=x. I can't validly cover the y axis in these coordinates, and the metric has infinities approaching the y axis in these coordinates. Is there anything wrong with the y axis?

NOTE: I do not say the EH is an artifact. I say any infinities there are an artifact of coordinates ill fitting for this region.

PeterDonis

Well, then the horizon of a black hole is one of those rare cases; you *can* make the infinity go away, completely, by using a better coordinate chart, and you can prove that all geometric invariants, i.e., all physically meaningful quantities, are finite and well-behaved at the horizon. This is a homework exercise in every GR textbook I'm aware of. It is not at all controversial.

Mike Holland

Arindamsinha, I had almost the same discussion in my topic "Black Holes - The Two Points of View" a few months back. I agree with your point of view, but have added a few provisos.

A lot of the problem centers around how you define "existence" and "now". Effectively, we live at the point of our past light cone. The light we receive from the universe around us defines our "now". We see the sun "now", but are actually seeing the light that left it 8 minutes ago. And similarly for the stars and galaxies. So when we say that Sirius exists, for example, we are really saying it existed 10 years ago.

Similarly with "existence". We may say that Napoleon is dead, and no longer exists, but an astronomer on a planet 200 light years away aiming his telescope this way would say that he can see Napoleon strutting around on Earh, and therefore he exists. Existence depends very much on one's point of view. We can say that things within our past light cone definitely did exist, as they can have a causal relationship with us, but outside that cone existence depends on the coordinate system chosen to describe the universe.

The result is that using our past light cones as our definition of "now", we can correctly say that Black Holes do not exist "now" in the universe we live in, and there are only slowly collapsing masses where they are forming. And this would apply to any observer at any tme, using that definition of "now", unless they have already (in their timeframe) fallen into a Black Hole. But there are many things going on in the universe which will never enter our past light cones.



Mike

DaleSpam

Mike, I don't know of ANY standard coordinate system which uses the past light cone to define surfaces of simultaneity. Can you provide a mainstream reference for one?

harrylin

Hi Mike, I saw some of that discussion, but most of it I could not follow - it was too abstract for me. I hope to be able to incite people to follow Einstein's example and discuss physical "clocks and rods".
Please don't include me in "we"! I mean with "now" and "exists" the same as "simultaneous" according to convention.

Note: PAllen started a topic about simultaneity.

Mike Holland

I am referring to the coordinate system we use all the time in our everyday lives. We observe a supernova, and say that it occurred in 2012. In this everyday sense it was simultaneous with our calendars reading 2012. But as it is 1000 LY away, we calculate that it "really" occurred in 1012. Someone passing by at 0.83c might say it is 500 LY away, and occurred in 1512.

I receive light from trees, the sun, stars, etc, and my mind builds up a view of the world around me, and this view is "now" as far as I am concerned. So I am seeing these things simultaneously, even though some of them may no longer exist - Betelgeus may have exploded a few years ago!

Simultaneity (sp?) depends entirely on the observer or coordinate system, and I rekon my view is as valid as any of them. But I do admit to having another view of "now" based on a theoretical line drawn vertical to my world line. How I draw this line and keep it vertical is based on my understanding of physics - GR in particular. And this theoretical "now" is mine alone, and need not apply to any other observers.

If you go back to Einstein's writings on SR, you will find that right through his work he uses this definition of simulteneity based on paths of light rays, as he proves that it is different for each observer. Is that mainstream enough?

Mike

DaleSpam

I am asking for a scientific reference. If you don't have one, then you should stop speculating. Everyday usage is not the same as scientific usage.

Mike Holland

Sorry Dalespam, I was editing my post as you replied, and added the last comment wehich I think covers that objection.

Mike

DaleSpam

He never once defines the past light cone as a surface of simultaneity. Post a reference that actually supports your idea of "using our past light cones as our definition of 'now'", or stop speculating.

Mike Holland

If you reread my post, I did not anywhere say that my past light cone defines simultaneity for me. Obviously, and as I pointed out in my post, things that appear simultaneous but are at different distances from me are not simultaneous.

What I am saying about that past light cone is that it contains events which are in my past and can have a causal effect on me. Everything outside that cone is theoretical for me. I "assume" that the sun is still there, although I have not seen it for 8 minutes. So all these outside events may be in my future, but some of them may never enter my past light cone and never occur for me, such as black holes forming (unless I jump into one). In this sense, the light cone is my "now", with the past inside it and the future outside.

Mike

PAllen

In case it isn't clear, what Dalespam is complaining about is that while there simultaneity is very much a matter of convention, it is universally accepted that the one restriction is that you don't consider causally connected events to be simultaneous. You have to pick between your forward and backward light cones. Einstein's convention basically takes exactly half way between for SR.

DaleSpam

Yes, you did:And you repeat it here:
The "sense" you are talking about is causality, and identifying causality with "now" is defining the past light cone as your surface of simultaneity. Not only did you say what I claimed you said, you repeated it and said it very clearly with lots of detail (but without any references).

Mike Holland

My past light cone defines simultaneous only in the sense that it defines what light signals arrive at my eye simultaneously. It does not mean that these light signals are from events that occurred simultaneously, but only that I SEE them simultaneously.

Due to the limit of the velocity of light, only events within my light cone can affect me in any way. So all photons emitted from all over the universe that arrive at my eye this instant have been emitted just as my light cone advanced to coincide with them. This defines my causal "now" without anything being simultaneous, except the arrivals at my retina.

Mike

DaleSpam

That is causality, not simultaneity. Stop trying to confound the two concepts. There is no scientific justification for doing so, and I think that you are well aware of that fact.

Mike Holland

Dalespam, I am not confounding the two. I have never claimed that they are the same. PLEASE read my posts and stop responding to what you THINK I have posted.

In the bit of my post that you quoted, I agree. When light from events reaches me, then those events can have a causal effect on me. Something that happened 10 LY away 10 years ago, and something than happened 5 LY away 5 years ago, will be on the same light cone and will be able to affect me (I will see them) at the same time. The only simultaniety is the effects arriving at me at the point of my light cone.

Do you not agree that all the photons I am seeing NOW from my present light cone arrived in my eye SIMULTANEOUSLY? And that consequently all the events on that light cone became able to affect me at the same moment? The only thing that is simultaneous is what happens here where I am. These events would not be simultaneous for anyone else.

NB Is there a word 'simultaniety'? Have I spelled it correctly? Simultaneousness??

Mike