Calculating Final Velocity of Matter into Black Hole Event Horizon

[eli_lied]

If this is in the wrong section, my apologies, but I'm wondering if it's possible, with known equations, to calculate the final velocity of matter accelerating into the event horizon of a black hole, and what those equations would be. I don't think this is an easy question, so any help is greatly appreciated!

 

[clamtrox]

It sure is, and it isn't that hard either as long as the black hole can be assumed not to rotate. From an observer infinitely far away (remember that speeds depend on the frame of reference) it looks like a particle falling towards a black hole approaches asymptotically the speed of light as it moves closer to the event horizon. Remember that for an outside observer, the particle never actually reaches the event horizon, but it 'freezes' just outside.

 

[eli_lied]

Wouldn't an assumption that the black hole doesn't rotate violate some law? Is there anything in the universe that doesn't rotate on some level? And as an observer, if nothing is observed at the point of impact amd beyond, does that mean it hasn't happened? That seems too convenient. The tree will fall regardless of who is there to see or hear it, and even that fall is a rotation, which returns to my original question...assuming all clamtrox reitterated about not rotating is true, what would the equations be?

 

[James Leighe]

Wouldn't an assumption that the black hole doesn't rotate violate some law? Is there anything in the universe that doesn't rotate on some level?

It rotates, it's just that the math is much more complicated when it does (you can't assume collinear motion and have to use vectors etc.). If you tried to enter the black hole perpendicularly to the axis of rotation (and assuming it was rotating) you would encounter an 'ergosphere' that would take you out long before you got close.

And as an observer, if nothing is observed at the point of impact amd beyond, does that mean it hasn't happened? That seems too convenient.

You cannot see what does not emit light. The reason you cannot see the person crossing the event-horizon (which is not a physical thing mind you, it's simply the mathematically defined point at which light cannot escape, a black hole is empty space sans a tiny / compact center) is simply because light cannot reach you from them as it's too dilated / red-shifted.

what would the equations be?

For a human being entering a non-rotating black hole you would use the relativistic velocity addition equation (google it). If it's collinear motion (a good simplification) the equations would be very simple... You would only need to know the mass of the black hole, the mass of the object falling in and the initial velocity of the falling object (if any).

 

[Dale]

If this is in the wrong section, my apologies, but I'm wondering if it's possible, with known equations, to calculate the final velocity of matter accelerating into the event horizon of a black hole, and what those equations would be. I don't think this is an easy question, so any help is greatly appreciated!

Well, in curved spacetimes the definition of velocity is purely local, so the question would be "velocity wrt what?".

 

[James Leighe]

Well, in curved spacetimes the definition of velocity is purely local, so the question would be "velocity wrt what?".

Probably the black hole.

The addition equation for collinear motion assumes that the velocity is relative to the two objects. Basically all he needs to do is use the relativistically corrected version of a simple projectile motion equation. I think... Anywhoo it doesn't seem like he is ready to calculate geodesics or tensors.

 

[Dale]

Probably the black hole.

That is interesting, I wonder if the curvature at the singularity would make velocity a definable quantity even locally.

 

[russ_watters]

That is interesting, I wonder if the curvature at the singularity would make velocity a definable quantity even locally.

I thought the defining characteristic of a black hole was that the escape velocity at the event horizon is C?

If that is true, isn't the answer to the OP's question simply 'approximately C'?

 

[Dale]

When people speak of a black hole I am never sure if they are talking about the event horizon or the singularity.

 

[granpa]

It sure is, and it isn't that hard either as long as the black hole can be assumed not to rotate. From an observer infinitely far away (remember that speeds depend on the frame of reference) it looks like a particle falling towards a black hole approaches asymptotically the speed of light as it moves closer to the event horizon. Remember that for an outside observer, the particle never actually reaches the event horizon, but it 'freezes' just outside.

how can a particle approach the speed of light and 'freeze' at the same time

 

[James Leighe]

I have a weird question...

If your going so fast compared to the black hole and approaching the speed of light would the black hole not evaporate (from time dilation) before you even reached the center? I guess it would need some very serious time dilation but isn't that what we expect?

 

[eli_lied]

Thanks for all the replies guys! This is going a long way to solving some independent research. And when I speak of a black hole, I'm talking about the singularity and the event horizon.

Also, as I understand it light is a tool used to view objects. In the absence of light, time still continues. I believe time is several times faster than the speed of light.

 

[DrGreg]

If this is in the wrong section, my apologies, but I'm wondering if it's possible, with known equations, to calculate the final velocity of matter accelerating into the event horizon of a black hole, and what those equations would be. I don't think this is an easy question, so any help is greatly appreciated!

The answer depends on exactly how you measure velocity.

For a distant observer, the answer depends on what coordinate system is used. In the "Schwarzschild" coordinates that are conventionally used for (somewhat unrealistic) non-rotating holes, the velocity slows down to zero as the event horizon is approached.

For an observer hovering very close to the event horizon, the falling object will be measured with a velocity slightly smaller than the speed of light as it passes the observer (using the observer's own clock and ruler for local measurement). But the speed will still drop to zero after it has passed the observer if the observer's coordinates are proportional to Schwarzschild coordinates.

It's impossible for anything except a photon to hover precisely on the horizon, so there is no meaningful answer in that case. Only an observer who is falling (or has already fallen) through the horizon can make a measurement at the horizon, and the measurement will depend on how the observer fell.

 

[EvilTesla]

Also, as I understand it light is a tool used to view objects. In the absence of light, time still continues. I believe time is several times faster than the speed of light.

I am very interested in time, and its dynamics.

So, I am curious, how would you define the "Speed of Time?"
Why do you say that Time travels faster than light? Why do you say that time has any velocity at all?

Remember Newtons laws F=ma. Which implies that for something to have a velocity, it must have a mass. Are you saying that time has mass?

Lastly, Time is a dimension, just like space. Its dynamics just seem to be a little different. So, your impling that a dimension has a velocity? Does Space have a velocity? Surely if time has a velocity than space could have a velocity.
(Though not necisarly, as I mentioned, temporal dynamics seem to differ from spatial dynamics)

 

[eli_lied]

I am very interested in time, and its dynamics.

So, I am curious, how would you define the "Speed of Time?"
Why do you say that Time travels faster than light? Why do you say that time has any velocity at all?

We rely on light to measure the passage of time. Using basic physics laws, if something has no motion, it remains in its position. If time stood still light would not reach us to allow us to determine frequency, yet if light stood still, time would not be affected. "In the dark room, I still age."

Remember Newtons laws F=ma. Which implies that for something to have a velocity, it must have a mass. Are you saying that time has mass?

https://www.physicsforums.com/showthread.php?t=353594 is the better yet not fully complete idea as to what I'm trying to prove. In that I'm trying to show that time is a result of a reaction of the pulsating energies of a singularity caused by normal space-time creating pressure on it. Like water putting pressure on a bubble. The particles that are ejected from the black hole are the ones I discuss in the previously mentioned post and to which the equation is related and ultimately cause the four major forces: strong force, weak force, electromagnetic force and gravity. It's a gross over simplification, but it's better to start small and rough and make it better than to start complex and have to take it apart to find the one bug.

Lastly, Time is a dimension, just like space. Its dynamics just seem to be a little different. So, your impling that a dimension has a velocity? Does Space have a velocity? Surely if time has a velocity than space could have a velocity.
(Though not necisarly, as I mentioned, temporal dynamics seem to differ from spatial dynamics)

I fully believe "time" has a velocity, that is, however, affected by the matter it passes through. I also believe space has a velocity since time is affected by the matter in space and consequently space itself which implies a force acting on both ends.

 

[EvilTesla]

We rely on light to measure the passage of time. Using basic physics laws, if something has no motion, it remains in its position. If time stood still light would not reach us to allow us to determine frequency, yet if light stood still, time would not be affected. "In the dark room, I still age."

This doesn't seem right to me.
Would you mind referencing somewhere, were a scientist has used light to measure the speed of time?

https://www.physicsforums.com/showthread.php?t=353594 is the better yet not fully complete idea as to what I'm trying to prove. In that I'm trying to show that time is a result of a reaction of the pulsating energies of a singularity caused by normal space-time creating pressure on it. Like water putting pressure on a bubble. The particles that are ejected from the black hole are the ones I discuss in the previously mentioned post and to which the equation is related and ultimately cause the four major forces: strong force, weak force, electromagnetic force and gravity. It's a gross over simplification, but it's better to start small and rough and make it better than to start complex and have to take it apart to find the one bug.

So, you're saying that all the four forces are due to a single particle.

If this is so, would you mind explain why we can only detect Photons for light, and not its equvilent for gravity, the strong force, and weak force?

Also, if this is so, should you not be able to derive the equations of the other four forces from you theory if you are true? If so, would you mind showing me the derivation of the coulombic force?

I fully believe "time" has a velocity, that is, however, affected by the matter it passes through. I also believe space has a velocity since time is affected by the matter in space and consequently space itself which implies a force acting on both ends.

Hmm...maby I am just having difficulty with your definitions.

To me, velocity is the distence something travels devided by the time it takes to get there.

Would you mind explaining what distence space is traveling through, and how long it takes for it to get there? I have a similar question for time, but we'll start with space.

IF space (and time) has a velocity, shouldn't it be measurable? I'm a bit lost on how you'd go about measuring the speed of space or time.

Further more, velocity is relative. When I say I go fifty miles an hour east. I mean I go fifty miles an hour farther east than the Earth does. Would you mind explaining what the velocity of time and space is relitive too? Is it relitive to itself? The other dimensions? Other universes (since that would be a diffrent space) perhaps?

Lastly, you said that space applies a force on both ends. I am curious as to the ends of what, and how much force it applies.

Thanks!

 

[eli_lied]

All of your questions are what I'm trying to answer. I am currently writing up a complete paper with drawings included to help understand my ecclectic thoughts lol. I love the devil's advocate when I'm researching and learning, and you are the best one yet!

I don't have a reference right now, but I could look one up. Anyways, aren't electron-microscopes using light to view the position of electrons albeit a very minimal source of light?

I've had to teach myself everything I know, but I've spent over ten years doing it mostly as a hobby and more recently as a serious past-time. However, lacking formal training shouldn't negate the possible potential and consequently the validity.

 

[Vanadium 50]

As a reminder to everyone, personal theories are allowed only in the Independent Research forum (under the guidelines posted there).