Idea about black holes... 4 spacial dimensions?

[RyanJ]

Idea about black holes... 4 spacial dimensions?

 

This is an interesting idea I had today while re-reading The Elegant Universe.

 

As one passes through the event horizon of a black hole they are destined to meet the singularity - there is no way to avoid it so their fate is destined to end there. Could this mean that time could be thought of as a spacial direction heading in the direction of the singularity in essence giving the black hole 4 spacial dimensions but no time dimension?

 

Thanks for the replies,

 

Ryan Jones

[5614]

Hmm, nah, I don't like it. Here's one example why: imagine a universe in which there is 1 black hole and 1 body. The body is stationary relative to the black hole and at such a massive distance that the gravitational effect is totally negligible. The body will never enter the black hole. That body's time is not heading towards the black hole, because it will never happen.

 

Although now I don't like that so much because one could argue that the time is heading towards the black hole but it is an infinite distance. But that is an invalid argument, because even after an infinite amount of distance it will never reach the black hole, so maybe the example is good.

 

Or are you saying that the time dimension could be considered as having a direction? But if we consider a particle (as opposed to a body) then the particle could quantum tunnel out of the black hole, so clearly it's fate or time doesn't have to end up in the blackhole.

 

Also the idea of within a blackhole the time dimension just disappearing and a 4th spatial dimension just appearing, sounds unlikely.

 

If this is not really what you were talking about can you explain a bit more.

[RyanJ]

HHmm - you make some good points!

 

Maybe it would be better to put it in this way: Time acts more like a spacial direction inside the black hole then outside.

 

That would allow for the quantum tunnelling effect. The odd thing is it does seem like a spacial dimension because it does have a direction. Outside a black hole there is no direction in which you can point to specify where time is going but inside the hole you could (Presuming you knew where the center was).

 

Any comments on that? If you would not consider it that way then how do you see it?

 

Cheers,

 

Ryan Jones

[5614]

You're saying that time is heading in a certain direction. If you could draw the time dimension as a line then you know where the end of the line is.

 

The quantum tunneling issue still arises... what if a particle (or in all improbability a whole body) tunneled out of the black hole, its fate, its time dimension cannot be said to have a definitve end, at least not for now.

 

Depending on the future of the universe all time may have an end or may go on forever.

 

Hmm, thinking about that, whilst a body may cease to exist as a normal body when it enters the blackhole the energy/matter that is does not cease to exist (because then it would violate the conservation of energy and/or mass). In a sense the body survives. In that sense maybe time is not ending.

[RyanJ]

The quantum tunneling issue still arises... what if a particle (or in all improbability a whole body) tunneled out of the black hole' date=' its fate, its time dimension cannot be said to have a definitve end, at least not for now.[/quote']

 

Yes - true. Can that happen on a larger scale? If it could (Which I'd bet it could) then it sort of invalidates the whole idea.

 

Hmm' date=' thinking about that, whilst a body may cease to exist as a normal body when it enters the blackhole the energy/matter that is does not cease to exist (because then it would violate the conservation of energy and/or mass). In a sense the body survives. In that sense maybe time is not ending.[/quote']

 

Well, it would still exist in the singularity made up of who knows what... as for time and space they would be distorted so much they could not be defined atleast thats my understanding of it.

 

There is definatly something more tangible about time in a black hole because it does seem to be more distinct, it does seem to be moving in the direction towards the singularity but the quantum tunneling issue raises some major problem with that idea as you have pointed out. Its actually more of a problem then I previously thought because by tunneling out of the hole it would esentialy fly from one timeline to alother timeline in the universe which seems very odd as it would just seem to have poped out of existance and appeared somewhere else...

 

Any ideas? That problem you pointed out is a big one for a number of reasons...

 

Cheers,

 

Ryan Jones

[5614]

As a single electron can quantum tunnel so could 2, so could an atom etc. etc. so theoretically a body could, but the probability will be infinitely small, probably so much so that we could say it would never happen... but theoretically there's only a probability stopping it.

 

Also have you ever thought about the definition of the word "singularity"... it is referring to a single point which cannot be divided into any further points. The height and length is 0, it is dimensionless. Just a random interesting thought.

 

Just a clarification, what do we mean by time? Because around a black hole spacetime is very weird. I wouldn't like to try and imagine/visualise spacetime around a black hole!

 

I spose so far I've been thinking more of a time line... a particle travels along a line, whilst it may seem to end in a black hole we don't know if it really does because the particle could escape and if it doesn't it eventually will when the black hole decays.

 

But this is all very different to talking about the structure of spacetime itself. Can spacetime end at a point? If you imagine spacetime as, well, everything, can it just stop somewhere in the universe where there is black hole?

[RyanJ]

But this is all very different to talking about the structure of spacetime itself. Can spacetime end at a point? If you imagine spacetime as' date=' well, everything, can it just stop somewhere in the universe where there is black hole?[/quote']

 

Yes - spacetime may not end there but it would be destorted well beyond anything we are used to, could we class that as a lack of time and space? We are used to linear time, who knows what would happen near the singularity - space and time are bent and mangled... its hard to define time in a linear manor let alone after its been destorted like that?

 

Also, I thought the singularity did have a dimension, for example if it were a spinning black hole should it not be a ring? Its hard to define one way or another either way its small and very dense.

 

Looks like this has tunrned into a debate, definitions are so hard to define

 

Cheers,

 

Ryan Jones

[Perturbation]

Idea about black holes... 4 spacial dimensions?

 

This is an interesting idea I had today while re-reading The Elegant Universe.

 

As one passes through the event horizon of a black hole they are destined to meet the singularity - there is no way to avoid it so their fate is destined to end there. Could this mean that time could be thought of as a spacial direction heading in the direction of the singularity in essence giving the black hole 4 spacial dimensions but no time dimension?

 

Thanks for the replies' date='

 

Ryan Jones[/quote']

 

Yes, space and time effectively flip: the radial coordinate behaves as if it were temporal and the time coordinate as if it were spatial. Paths assumed by those bodies confined to speeds below c, i.e. massless bodies, are known as space-like. This means that upon entering the innerds of the black hole these space-like paths become time-like, paths assumed by bodies confined to speeds above c, and visa versa. (We don't get four spatial dimensions like you're suggesting though.)

 

I wouldn't like to try and imagine/visualise spacetime around a black hole!

 

Look up Kruskal-Sziekeres (not sure about the spelling) coordinates. Offers a more coherent depiction of the space-time geometry about a Schwarzschild black hole' date=' much more than the regular spherical polar coordiantes, which are rather elluding when it comes to Schwarzschild geometry.

 

Also, I thought the singularity did have a dimension, for example if it were a spinning black hole should it not be a ring? Its hard to define one way or another either way its small and very dense.

 

Yep, for Kerr black holes (or any rotating black hole [static]) the singularity is a ring. A singularity is not so called because the dimensions of it are singular, i.e. pointlike. A singularity is called this because it's the region where the curvature, which is essentially the gravitational field-strength of the hole, diverges to infinity. In the simple case of a non-rotating, spherically symmetric (stationary) black hole, that is the well known Schwarzschild black hole, the curvature diverges to infinity as one tends towards the centre of the black hole, so the singularity of this variety of hole is a point. For more general holes, however, the region where this divergence occurs needn't be a dimensionless point. To stress the point again: the singularity is where the field is infinite.