Print

Please login or register.
1 Hour 1 Day 1 Week 1 Month Forever
Login with username, password and session length

[Virex]

I'm stuborn about the physics of black holes

Besides that, since a black hole is a singularity, there is no such thing as directly into the singularity (it's infinitismally small), so any light shot "almost" directly at the singularty, and then it'll turn around and go back to the other edge of the event horizon [...]

Except that the inexorability of light falling 'towards' the singularity (see below for an agreement, as opposed to an objection) means that it's not a matter of light 'sloshing around' within the Event Horizon.  More like... (well, I suppose intentionally like..., seing as it's supposed to be a model of same) those "gravity wells" that you can send balls into where they can loop around.  Down to a certain point, you can engineer an eliptic (give or take loss of energy through air and material resistance) coming back up to the level of release, but after a certain depth you can only really see them going downwards (although, due to intrinsic classical effects its a fast orbital barely downwards rather than dragged mostly 'down').

Or perhaps, to remove the classical effects altogether, don't use the ball and instead painstakingly draw a line on the surface.  A straight line (across the constraints of the warped surface).  Some lines will merely go 'around' the hole, but some lines you draw will lead down into the funnel and never emerge.  The distinct diameter of hole which no line can pass without ending up 'only going downwards' from then on is the event horizon.  (Even then, there are flaws in the analogy, but different flaws.)

That was quite exactly what I was talking about. The light is locked inside the event horizon, but inside that, there has to be some kind of trajectory it follows, unless//untill it loses it's identity. That is, of course, assuming that "inside the event horizon" is a valid discription, which you discuss later in this post.

This realtes to something else I thought of. Generaly, a singularty is assumed to actualy exist. But wouldn't the space-time curving effects of gravity prevent matter from actualy reaching the singularity itself?

Now, this is more or less relevent to a prior reply of mine to someone regarding infinities.  In a perfect 'model' gravity well (the 'toy' ones are obviously finite in depth, and are probably designed to asymtotically close to 'just larger than the ball-size' anyway), the slope gets steeper and steeper (close to, but not vertical) and the slice across at that level reveals a smaller and smaller hole (close to, but not, of zero size) but it's an infinitely deep slope which never quite closes.  Thus there is no part of the model that relates to the point of the singularity.

However...

After all, the closer matter (and energy) comes to the singularity, the more time dialatation it's going to experience[...]

Beyond the event horizon, time dilation isn't really applicable any more, in the same manner.  A simple (wrong, but indicative) explanation is that v>c, so root(1-(v^2/c^2)) in the various equations is root(1-(>1)) is root(<0) and thus an imaginary number.  Which (given time works like an 'imaginary' dimension in various other formulae encompassing space and time coordinates) lends support to the whole "time becomes space, space becomes time" idea.

Erm, what V are you talking about? V_escape > C, but that's not a real velocity, only a limit. I do think I get what you mean though, I was mistakingly assuming that the problems with black holes stem from the singularity itself, while actualy everything inside the event horizon is "messed up", or at least that's what your reply indicates.

It's been said that Hawking radiation would cause a black hole to evaporate long before you reached the singularity, but why is this not true for the matter that is to form a new black hole?

I suspect because it's not a matter of the mass needing to be "at" the future singularity point to create the black hole, but that sufficient mass finds itself within either the event horizon or Schwarzchild radius.  (Actually, isn't that the definition of the SR?  I forget.  Must check Wiki or something at some point. , there then forms a 'singularity-centred' funnel (where previously there was just a dimple of whatever depth).  And (through quantum uncertainty) no actual matter or energy (e.g. baryon, electron, quark, photon, gluon, Higgs boson, graviton, whatever) will be precisely 'at' the virtual point in space that is the 'singularity-centre' to cause complications, and now you just have to worry about whether the energy and matter that form (or later fall into) the black hole loses its identity or not in the warping of space-time.

I've got the feeling I should realy shut up now, but I'll ask anyway: if there is no matter at the singularity point itself, isn't that point supposed to be a location with zero space curvature? After all, assuming an uniform distribution along whatever dimention there is, there is an equal "amount of gravity" pulling from each direction. Wouldn't you end up with a second event horizon inside the black hole?

[Neruz]

I would say that given the known properties of a Black Hole, 'inside the event horizon' may well be entirely nonsensical.

[G-Flex]

A gravitational singularity is where space curves infinitely down at one point, making it discontinuous. So yeah, nothing reaches it, it just keeps getting closer asymptotically.

That's my horrible explanation of it, anyway.

[Starver]

Beyond the event horizon, time dilation isn't really applicable any more, in the same manner.  A simple (wrong, but indicative) explanation is that v>c, so root(1-(v^2/c^2)) in the various equations is root(1-(>1)) is root(<0) and thus an imaginary number.  Which (given time works like an 'imaginary' dimension in various other formulae encompassing space and time coordinates) lends support to the whole "time becomes space, space becomes time" idea.

[citation needed]

For what bit?  Ok, I'll try and do it all then.

Taking Time Dilation from Wiki (well, might as well, if you're doing the whole "[citation needed]" bit you'll see the "root(1-(v^2/c^c))" component, or equivalent.  Which leads naturally to an imaginary number.  (You don't need that explained, do you?)

## And at this point I was chucked out of work, went home, wrote the rest up properly and then promptly forgot to bring my memory stick in this morning, so here's a brief version: ##

In time-like curves or 'world lines' (it's hard to search for an equation) you have dX^2 + dY^2 + dZ^2 + dT^2 = 0 if we treat each dimension as a type of 'spacetime' measurement.  If something is not moving (zero dX, dY and dZ) with respect to a frame of reference, then dT (the difference in the passage of time compared to that frame) is zero.  If there is movement then classically you're in a t=t_o.root(1-(v^2/c^2)) situation (expressed differently but interchangably in Wiki, again) by other measures, a difference in time.

But with movement in dX, dY and/or dZ (which are interchangable, all movement through a single axis equivalent to movement through any other axis, or combination) mean that either (dX^2 + dY^2 + dZ^2) sums positive and dT^2 is negative, or vice-versa.  At this level, it doesn't matter which way round, but we're used to real measurements of distance, and we're used to time being ineffible (although the apparent irreversibility of time isn't anything to do with this at this point), so go with me in suggesting that the measure of dT is a difference of an imaginary number.

At the speed of light, in fact (whether entirely represented by dX, dY or dZ; or a combination of motions adding up to that) the units we apply to the 'space' elements of the spacetime equation reflect that dT must be the imaginary complement to the light-speed idea.

You'll note that the formulae convert quite well into other common forms of spacetime equation.


Now, consider "beyond the Event Horizon".  'Out here' we can describe space by three coordinates in multiple ways.  In the x, y and z cartesian manner or with polar coordinates (but still with three indicators, e.g. longitude, latitude and altitide/radius).  And in space-time (x, y, z, t), except that is generally accepted to have an inevitability to it.

But beyond the event horizon, the 'inevitable' dimension is radial (everything must fall inward), and physics is arguably such that all usual answers are imaginary versions off their prior selves, and an imaginary version of the initially imaginary time dimension means you now have a real dimension.  That's a leap of faith, there (this is the re-written explanation and I spent a lot of time on this last night which I'd rather not redo), but how about the proposition that the space-like dimensions are now time-like and the time-like one is now space-like?

Interestingly, I remember an article in New Scientist (circa 1993, from the memories I associate with it) about the fact that in a 'three time and one space dimension', tachyons are the overwhelmingly predicted phenomena.  And FTL particles such as tachyons are presumed to be create imaginary values in the standard Lorentzian formulae.  And, furthermore, if the slope of space-time at the event horizon were such that a particle capable of light-speed travel would (if attempting to head directly outward) stand still in a very unstable position of equilibreum, then within the EH space-time would be pulling all captured particles and energies beyond (classical) light-speed.  Admitedly in a very non-classical manifold of space.


So, that's a summary.  I wish I had access to my old university physics tutor, as I'm sure I've skipped over some things important to the layperson and grossly misrepresented other things important to the currently practicing experts among you.

And, of course, I'm no TimeCube person.  The above's just an interpretation, and only really involves the Twighlight Zone beyond the EH, so I ackknowledge it's speculative at best.  Probably superceded by something else that's arisen in the last couple of decades that I've not heard of.  (Not including all other alternative universal explanations, like those including M-dimensional branes.)


[edited because I accidentally invoked a tag in one of my formulae...]

[Starver]

Heh, I have this thing against people saying wrong things (that can't be proven wrong easily) just to sound smart.

I do try to indicate where I'm actually going into speculation, but reckon I probably look like one of these.  Especially when I don't know at what level to place (or can't consistently keep at that level) my explanation.  One minute explaining a simple formulaic matter and the next leaping over an entire concept with little more than a "trust me".

Apologies for when I do that.  My stream of consciousness doesn't have a good hand-brake.

[Starver]

I'm stuborn about the physics of black holes

Sometimes I think I just blather about it.  I reckon few people would argue with that.

Erm, what V are you talking about? V_escape > C, but that's not a real velocity, only a limit. I do think I get what you mean though, I was mistakingly assuming that the problems with black holes stem from the singularity itself, while actualy everything inside the event horizon is "messed up", or at least that's what your reply indicates.

In that version, 'effective velocity', really.  In a classical physics example, anything beyond V_escape... well, escapes.  Force in the form of gravity is applied to an object attempting an escape (even those succeeding) to slow it down.  But in 'gravity well' physics where it's a straight line on the topology of a distortion in space, you can consider it a constant speed but affected by the slope of the well.

If the slope of the well beyond an EH is sufficient to prevent light from escaping, that you are removing 'c'-or-greater outward veolicty, or giving things without a sufficient outward speed travel a greater-than-'c' (from a classical POV, only) inward motion.  Which is how (inward)V could be considered greater than C.

Spot the flaw, however.  And (for bonus points) spot the solution.  (There's a possible flaw to the solution, too, but... beyond where I've gone with that idea.)

I've got the feeling I should realy shut up now, but I'll ask anyway: if there is no matter at the singularity point itself, isn't that point supposed to be a location with zero space curvature? After all, assuming an uniform distribution along whatever dimention there is, there is an equal "amount of gravity" pulling from each direction. Wouldn't you end up with a second event horizon inside the black hole?

Quick answer: When the hole was being formed, it was a region (the Schwarzchild Radius) which is 'deemed' to have so much mass in it that this region was no longer part of the external universe and was thus becomes an inescapable gravity-trap.

Slow answer: With a hyperbolic curvature, there is less space (around a given radius) the further 'down' you go there's more matter sitting in less space, and because in at least one sense (inwards-vs-outwards) there's not equal mass either side of your point, you're still sitting on a gravity gradient.  With the mass 'further down' the curvature moving 'faster' (if that's a useful term in this environment) and thus exhibiting speed-induced mass increases of some form to maintain "more mass inwards than outwards" conditions.

Slowest answer: If matter (and energy) is still discrete enough to identify, then you'll find some point between Black-Holed particles where gravitational pull cancels out, just like transient Legrangian points in the Earth/Moon/Soon system.  But matter and energy of all kinds is considered wave-like at small distances, smears out and thus there's no point without the massively 'oversmeared' density.  Which sort of shows that there probably wasn't 'nothing' at the point of the alleged singularity formation, but at the same time supports that when spacve-time rent at the spot of this singularity, everything that went on to compose the black hole's mass could have been not-quite-there.

Off-the-wall answer: hyperbolic curve opens again after infinity into a dimension somewhere/when else, in this universal manifold or another, and that's the second event horizon?

Another possible answer: The universe 'inside' a black hole is a viable universe with twisted physical properties that considers the Event Horizon to be an EH (in the opposite direction) to 'our' region of strange spacetime (strange to an observer in that universe.  Some theories require an 'arrow of time' in the opposite direction to ours.  It gets wierd like that.

But it's a tricky one to be precise about.  Certainly.  Depends what you believe in.  And I think the trickiest area of discussion are the borders.  In space alone, the EH itself.  In time alone, the moment of "Blackholification" and the one where it finally evaporates.  Though if you consider it as an elongated boundary sphere in time and space it sort of works.  At least until you want to include merging black holes into the equation.

[edited because I messed up quotes.]

[dreiche2]

[citation needed]

For what bit?  Ok, I'll try and do it all then.

Sorry, I should have clarified. I do not think there is ever a case in relativity where you plug in v>c. Tachyons might be an exception, but whether they exist and if so what that actually means is highly obscure. I would highly question any argument that explains a situation by referring to imaginary time.

And overall, sorry but I have to doubt that you really know what you are talking about. Which you seem to acknowledge, but what's the point of making seemingly formal arguments then?

In time-like curves or 'world lines' (it's hard to search for an equation) you have dX^2 + dY^2 + dZ^2 + dT^2 = 0 if we treat each dimension as a type of 'spacetime' measurement.

I don't know what you mean. If we are talking about measurements from within a given frame of reference, then the metric of a Minkowski vector is computed as (scaling c to 1)

s^2 =  r^2 - t^2,

i.e. you're missing a minus sign. Time-like world lines have s^2 < 0. Equal to zero would be light-like.

Time dilation is however an effect that comes from a change in coordinate systems. Are you talking about that?

But with movement in dX, dY and/or dZ (which are interchangable, all movement through a single axis equivalent to movement through any other axis, or combination) mean that either (dX^2 + dY^2 + dZ^2) sums positive and dT^2 is negative, or vice-versa.

Well, again, you miss a minus sign. In general, measuring things within a frame of reference using the Lorentz metric as defined above never gives you 'imaginary time'. Doing a change in frames of reference does give you imaginary time if you assume a relative speed of v>c, which of course you're not supposed to do.

At the speed of light, in fact (whether entirely represented by dX, dY or dZ; or a combination of motions adding up to that) the units we apply to the 'space' elements of the spacetime equation reflect that dT must be the imaginary complement to the light-speed idea.

 

Now, consider "beyond the Event Horizon".  'Out here' we can describe space by three coordinates in multiple ways.  In the x, y and z cartesian manner or with polar coordinates (but still with three indicators, e.g. longitude, latitude and altitide/radius).  And in space-time (x, y, z, t), except that is generally accepted to have an inevitability to it.

But beyond the event horizon, the 'inevitable' dimension is radial (everything must fall inward), and physics is arguably such that all usual answers are imaginary versions off their prior selves, and an imaginary version of the initially imaginary time dimension means you now have a real dimension.  That's a leap of faith, there (this is the re-written explanation and I spent a lot of time on this last night which I'd rather not redo), but how about the proposition that the space-like dimensions are now time-like and the time-like one is now space-like?

 

So, I'm no expert with black holes or general relativity. However, my current understanding, and I would like to see evidence/ citations to the contrary, is this (although granted wikipedia is confusing in some parts about this):

1. The event horizon marks a boundary from within which events can not be observed by an outside observer, as all emitted light within will stay within.

2. Apart from that, there is nothing extremely weird going on inside the horizon, not counting the weird singularity itself. No imaginary times, no division by zeroes, no infinities, as far as I can see.

3. It is actually possible to see something cross the event horizon, seen from an outside, stationary observer. Or rather, you couldn't see it, because the light would never properly reach you, but if you were to compute things in your frame of reference, you would compute the path of the object cross the horizon at some point.

I am pretty sure about 1. and 2., so all imaginary time discussion is invalid IMO. I'm not completely sure about 3., nor about what happens from the point of view of someone approaching the horizon (option one: he crosses it, no problem. Option two: The horizon keeps receding away in front of him; but this is not in contradiction to what happens from in an outside frame of reference, because where the horizon is is again relative).

Finally, even the singularity is not necessarily a proper singularity, because either, as some sources seem to suggest, it's just an approximate description, or, at some point quantum mechanics will come in the way, similarly to the case of the charge of an electron being concentrated in an infinitely small point classically.

[Sean Mirrsen]

I didn't want to chime back in here with my unscientific views, but decided to spice the discussion up a bit. In the Multiverse, a black hole is just a superparticle. When matter fails to exist due to overwhelming force, the result is a construct of all the energy contained in the original matter, a supercomplex particle. Since for a 'non SR compliant' universe C is not the limit, this particle spins at speeds far exceeding that of light, balancing its structure against the gravity it generates with sheer velocity. The event horizon is nothing special, it's just a radius around the black hole where any naturally occuring emissions will completely fail to pass through due to gravitational distortion reducing their waveforms to nothing.

The above has no ties to the previous discussion on relativity, I just wanted to share some off-universe lore.

[DreamThorn]

Overall, I would say that Starver has been giving the most well-researched and scientifically approved explanations in the whole thread.

In electrodynamics, treating time as a space-dimension, but with imaginary values, Maxwell's four equations become one four-dimensional equation without much fuss.  (IIRC)  I feel certain this will work even better when one adds relativity, since it was Maxwell's electrodynamic theories that led to its invention in the first place.

So, if you were treating time as being real and then find you need an imaginary amount of time, you would end up with a negatively oriented space dimension. (i * i = -1)

No idea which direction that would be, though.

And, an interesting thing about space-time and black holes, which I think I read in Stephen Hawking's "A briefer history of time":

The fact that no real-massed particle can enter or escape from a black hole in our frame of reference (ignoring hypothetical Hawking radiation), would mean that the space-time inside the black hole seems non-existent to us.  If we however fall into the black hole, our frame of reference is changed to one from where we can enter the black hole, and the light from inside can also exit and reach us there.  From the outside we would still not seem to be entering, and light would still not seem to be exiting.  This is of course time dilation's effect.

[dreiche2]

Jesus C on a motorbike. I give up. Have fun with your imaginary (pun!) science, guys.

EDIT: I mean really:

mean that either (dX^2 + dY^2 + dZ^2) sums positive and dT^2 is negative

He is using the wrong formula! And then from there... Well-researched and scientifically approved???

Whatever, guys. 

Edit 2:

So, if you were treating time as being real and then find you need an imaginary amount of time, you would end up with a negatively oriented space dimension. (i * i = -1)

I mean. What. The. 

[Cheeetar]

I have no idea about mathematics apart from the most basic things, but I think he's referring to two lines on a graph. The way to prove that they are perpendicular is if their gradients multiply together to reach -1.

[dreiche2]

Aarrrghghhg

I have no idea about mathematics

Agreed.

[Cheeetar]

I'm helping.

[bjlong]

I say we change to an entirely different subject. Like lasers.

[dreiche2]

gradients... -1.... just no.


If you're talking about two vectors, and compute the scalar (/dot) product, and they are perpendicular, you get 0. Not -1. 0.

-1 one would be anti-parallel.

Nor does this help anything with what Dreamthorn just said about imaginary time leading to 'negatively oriented' space dimensions. Which does not make sense: neither the assumption, nor the consequence, nor that the consequence would follow from the assumption.