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The event horizon of a black hole accelerates at the speed of light.
Quote from: MikeS on 05/05/2012 08:22:28The event horizon of a black hole accelerates at the speed of light. The event horizon of a black hole is stationary, i.e. it doesn't move at all. It only move relative to the observer who is in free fall. That the event horizon is stationary and the obserer in free fall is not a paradox because they move relative to one another, hence the relative in Einstein's General Theory of Relativity.
The event horizon is stationary in the SPACE dimension of space-time but is accelerating in the TIME dimension of space-time so it is moving in space-time.
Quote from: MikeS on 06/05/2012 05:13:25The event horizon is stationary in the SPACE dimension of space-time but is accelerating in the TIME dimension of space-time so it is moving in space-time.It is unclear to me how you came up with the notion that the space dimension of spacetime is accelerating in the time dimension. Seems to me that the event horizon of a black hole in Schwarzschild coordinates is a 3-D spatial surface. However you're speaking of a different coordinate system. Please provide a derivation of your assertion or if I'm wrong please a derivation of what I did wrong. After that it might take a month or so to (1) finish up my study of Dark Matter and (2) study your claims in detail. It's been a extremely long time since I studied black hole so be complete I'll have to take time to study the spacetime of black holes closely.
Event horizons are more or less stationary
I will take a stab on it Mike. Seems as if you want to define something as 'moving in time' although stationary in a positional space you are assuming some definitions. The first one is that the arrow exist as a 'force/stream' that always transports us forward. Doing so there are no stationary positions in space, so even when we define something as unmoving it will still move inside that arrow. It's not that different from a lot of other ideas that I've seen regarding the way SpaceTime seems to be interconnected.but there is a difference, as I see it, in how you think of it and Einstein did. Einstein assumed a continuum where all aspects of SpaceTime in some mysterious fashion was interweaved. I don't think he saw it as 'split able', instead he saw SpaceTime as a expression that was whole in itself, a four dimensional continuum.As for 'the arrow' accelerating I'm more confused. When it comes to the arrow having a constant defining it, then we must use a 'clock' to do so, and as 'c' is the clock of choice here, splitting 'c' into even chunks we can define it as such- But that is just the best 'clock' both you and me can come up with. It does not state what a arrow comes from, as in a origin, neither does it tell us anything more than this seems the preferred way of describing a arrow inside SpaceTime. As some first ideas this is, I'm still feeling rather slow from yesterdays excursions
If you use 'c' defining the arrow then it never 'accelerates' for you. And as it your measurements that decides any proportionality in a comparison between frames of reference the best you can state is that 'the arrow' seems to be different when looking at some other frame of reference. But going there it won't be.
So in a way Einsteins view must be the right one, it's a unsplittable four dimensional continuum that you carry with you, expressed through measurements defined by your local 'clock' and your local 'ruler'. And you can't 'move' outside this definition inside SpaceTime.
I think we had that discussion before?To assume that the event horizon is equivalent to 'c' you also need to to define what happens with in-falling mass. In Einsteins universe that mass will pass the event horizon, as observed from its own frame of reference, although there is a lot more to that as 'apparent horizons', gravitational effects etc. But it will pass, and it shouldn't exist at all at that border, if the equivalence to 'c' was at the Event horizon. I too see a equivalence Mike, but I would place it at the singularities center if so. And that place must, if this is correct, be a place where everything we know (physics etc) breaks down.As for living in a non inertial frame I'm not sure how you mean. A inertial frame is any uniformly moving frame as I think of it. That we call it 'inertial' although those frames can be measured to have different uniform motion, relative Earths for example, state a equivalence between them that makes uniform motion very strange to me, or motion in general. Then we have accelerations that gives us the equivalence to a gravity. You could assume that it is a question of inertia expressed in the matters particles adapting new relations relative each other, time dilated as well as Lorentz contracted though. I'm wondering about that as we write? If that was so, then you might assume that uniform motion, wherein no 'gravity' is existent if ignoring matter itself, is the natural state of the universe. But matter has the ability to distort the 'space' which might be seen as a consequence from the way it 'binds' energy, if we assume energy to be some universal coin of measure.As long as you don't move you are in what I would call a inertial frame, loosely speaking that is. But as we constantly move you might want to define it as 'non-inertial' any way It's all a question of your definitions there, but they have to be very strict if you want people to see how you think.
As the arrow being entropy?I got to admit that I'm not sure what entropy stands for any more. Some want to define the arrow as 'entropy' as if the arrow was something living, constantly 'growing'. I prefer to avoid that word myself, because a lot of definitions of what entropy is seems to exist. It's a little like the idea of 'information' which I, although simpler to understand, also finds hard to melt. If we would be 'information' what about writing a equation on a ice cube? Where did it go, the equation I mean? And maybe that can be used for questioning entropy too?
My own view on it Mike is related to 'energy'. Even though we can't hold a pound of 'energy' in our hands it exist as a conceptual measure of something changing. And in a acceleration you spend 'energy', in a uniform motion you don't.
The event horizon of a black hole accelerates at the speed of light. Therefore the black hole accelerates at the speed of light( but is hidden behind the EH).General Relativity states that mass can not accelerate up to the speed of light. Matter being consumed by a black hole accelerates up to the speed of light at the EH.Is this a paradox? If not why not?