Limitless Momentum of Black Holes

[Sveinbjoern]

I am a hobby reader/listener of pysics, astronomy, special relativity, black holes and more. And a question arose that no amount of YouTube has touched on.

Sorry if this is just a stupid question from a hobbist but it truly has me stumped. Or maybe I just have been taught by oversimplification.. Anyways! The question:

At the event horizon not even light can escape... but anything with mass should!?

Essentially my question boils down to: Is there a limit to the amount of energy that can be given to a mass as speed? Or asked in another way can momentum be increased without limit?

As I understand mass can be accelerated with indefinite amounts of energy approaching the speed of light. Also giving that this mass would need the opposite amount of energy to stop.

Given an object for example a bit of non-interacting dark matter accelerated standing still right next to a black hole should reach in AND end up on the other side outside the event horizon. Energy preserved. Essentially not caring about the event horizon. Starting as far out as it could be attracted by it and gaining the speed to end up on the other side equally far from the senter of mass of the black hole. Yes?

The same applies to normal matter. Approaching the black hole with sufficient momentum. Never reaching the speed of light but having enough energy that the black hole can not hold it. As long as it does not collide with stuff... it should be possible to skim into the event horizon and out as long as you HAVE mass? The pull of the black hole must be limited but as long as the energy you can put into a massive object is not you must be able to visit the inside of the event horizon and get back out...

 

[Orodruin]

Essentially my question boils down to: Is there a limit to the amount of energy that can be given to a mass as speed? Or asked in another way can momentum be increased without limit?

No, there is no such limit. However, this does not help because no matter how much energy you give a mass it will not locally travel faster than the speed of light and this is what it would need to do to escape from within the black hole's event horizon. If light cannot escape, then nothing else can either.

 

[Ibix]

At the event horizon not even light can escape... but anything with mass should!?

Light is always the fastest thing (at least locally). If you had light not getting out of the black hole but something massive getting out, then there would be a situation where a massive object could overtake a light pulse. In other words the massive object would be traveling faster than light - forbidden in relativity.

Given an object for example a bit of non-interacting dark matter accelerated standing still right next to a black hole should reach in AND end up on the other side outside the event horizon.

The interior of a black hole does not work that way. Once you cross the event horizon, there are no time-like paths back out. Full stop.

In fact, in a non-rotating black hole, the singularity isn't a point in space but rather more like a point in time. Once you cross the horizon you can no more avoid the singularity than you can avoid Monday morning. Rotating black holes are more complex, but you still can't escape. The interior isn't the simple spherical region you might be imagining.

 

[Sveinbjoern]

I am a hobby reader/listener of pysics, astronomy, special relativity, black holes and more. And a question arose that no amount of YouTube has touched on.

Sorry if this is just a stupid question from a hobbist but it truly has me stumped. Or maybe I just have been taught by oversimplification.. Anyways! The question:

At the event horizon not even light can escape... but anything with mass should!?

Essentially my question boils down to: Is there a limit to the amount of energy that can be given to a mass as speed? Or asked in another way can momentum be increased without limit?

As I understand mass can be accelerated with indefinite amounts of energy approaching the speed of light. Also giving that this mass would need the opposite amount of energy to stop.

Given an object for example a bit of non-interacting dark matter accelerated standing still right next to a black hole should reach in AND end up on the other side outside the event horizon. Energy preserved. Essentially not caring about the event horizon. Starting as far out as it could be attracted by it and gaining the speed to end up on the other side equally far from the senter of mass of the black hole. Yes?

The same applies to normal matter. Approaching the black hole with sufficient momentum. Never reaching the speed of light but having enough energy that the black hole can not hold it. As long as it does not collide with stuff... it should be possible to skim into the event horizon and out as long as you HAVE mass? The pull of the black hole must be limited but as long as the energy you can put into a massive object is not you must be able to visit the inside of the event horizon an

No, there is no such limit. However, this does not help because no matter how much energy you give a mass it will not locally travel faster than the speed of light and this is what it would need to do to escape from within the black hole's event horizon. If light cannot escape, then nothing else can either.

I am not asking matter to move faster than lightspeed.. just faster than the beams of light present. Like in a nuclear reactor! Where the water breaks down the speed that light is localy traveling and high energy particles can move faster. I understand that light cannot escape but what is holding high energy matter? It should not need more speed only more energy. What part of dark hole property am I missing to understand this?

 

[Sveinbjoern]

Light is always the fastest thing (at least locally). If you had light not getting out of the black hole but something massive getting out, then there would be a situation where a massive object could overtake a light pulse. In other words the massive object would be traveling faster than light - forbidden in relativity.

The interior of a black hole does not work that way. Once you cross the event horizon, there are no time-like paths back out. Full stop.

In fact, in a non-rotating black hole, the singularity isn't a point in space but rather more like a point in time. Once you cross the horizon you can no more avoid the singularity than you can avoid Monday morning. Rotating black holes are more complex, but you still can't escape. The interior isn't the simple spherical region you might be imagining.

Well this is perplexing however that is not a big surprise given the subject matter. If locally light has to be the fastest then how can charenkov radiation exist. Where light moves slower due to being in water and high energy particles travel faster. I guess we are onto what I am not getting. What kind of mechanism are you talking about when you say light has to be the fastest locally?!

When it comes to the special relativity and time dilation issues I simply take the viewpoint of the massive object. It experiences the time dilation but does not stop as it can never reach the speed of light. Sure when it exits the universe is a lot older... but hey it got out of a black hole I think the easiest way is to imagine non-reacting dark matter that enters a black hole... what happens to it?
I cannot understand what mechanism that stops matter from doing this. Sure any object in the pull of a black hole would have to propel itself to ever escape a black hole but that is true of any heavy object.. and again for the massive object time cannot stop! As it has mass and can never reaching linseed no matter how hard it is pulled... I know I am missing something... but I do not know what...

 

[PeroK]

What you are missing is the geometry of the situation. Particles with mass travel on timelike paths. At the event horizon, all timelike paths have decreasing $r$. Light (in a vacuum) follows a null path. There is a "stationary" null path $r = 2M$ on the event horizon.

Inside the event horizon, all timelike and null paths have decreasing $r$.

 

[Ibix]

I am not asking matter to move faster than lightspeed.. just faster than the beams of light present.

There is no medium around a black hole (or there need not be, anyway). It's a vacuum, so light is doing c. It's just that the curvature of spacetime is such that c is not fast enough to get anywhere in an outwards direction. So anything that did escape would have to overtake a light pulse - be traveling faster than c.

Like in a nuclear reactor! Where the water breaks down the speed that light is localy traveling and high energy particles can move faster.

The speed of light can mean two things in relativity. One is the constant c, which is always 3x10⁸m/s. The other is the speed at which light happens to be traveling in some place due to the effects of a medium, which may be less than c. It's the first definition that is relevant here (there need be no medium around a black hole, and it's the constant c that appears in the maths for the location of the event horizon), so your fuel rod storage pools example isn't applicable.

I understand that light cannot escape but what is holding high energy matter?

The curvature of spacetime. There are no outward paths for anything that is not moving faster than light, once you are inside the event horizon.

It should not need more speed only more energy. What part of dark hole property am I missing to understand this?

I don't know. I suspect you are thinking of gravity as a force pulling things downward. Relativistic gravity doesn't work that way. It's just the curvature of spacetime is such that light cones "tip over" (scare quotes because this is a coordinate-dependent description) as you approach the event horizon, and all future-directed paths remain below the event horizon.

 

[PeroK]

Well this is perplexing however that is not a big surprise given the subject matter. If locally light has to be the fastest then how can charenkov radiation exist. Where light moves slower due to being in water and high energy particles travel faster. I guess we are onto what I am not getting. What kind of mechanism are you talking about when you say light has to be the fastest locally?!

When it comes to the special relativity and time dilation issues I simply take the viewpoint of the massive object. It experiences the time dilation but does not stop as it can never reach the speed of light. Sure when it exits the universe is a lot older... but hey it got out of a black hole I think the easiest way is to imagine non-reacting dark matter that enters a black hole... what happens to it?
I cannot understand what mechanism that stops matter from doing this. Sure any object in the pull of a black hole would have to propel itself to ever escape a black hole but that is true of any heavy object.. and again for the massive object time cannot stop! As it has mass and can never reaching linseed no matter how hard it is pulled... I know I am missing something... but I do not know what...

You have to distinguish between the universal constant that is the speed of light in a vacuum $c$ (nothing can move faster than that) and the speed of light in a material, which may be less than $c$. If light is influenced by its medium and slows down, that doesn't mean that everything else must be slowed down even more, hence Cherenkov radiation.

In curved spacetime, vectors (including velocity) become a local concept. Which is why we talk about the "local" speed of light: the speed as measured locally.

 

[Sveinbjoern]

There is no medium around a black hole (or there need not be, anyway). It's a vacuum, so light is doing c. It's just that the curvature of spacetime is such that c is not fast enough to get anywhere in an outwards direction. So anything that did escape would have to overtake a light pulse - be traveling faster than c.
The speed of light can mean two things in relativity. One is the constant c, which is always 3x10⁸m/s. The other is the speed at which light happens to be traveling in some place due to the effects of a medium, which may be less than c. It's the first definition that is relevant here (there need be no medium around a black hole, and it's the constant c that appears in the maths for the location of the event horizon), so your fuel rod storage pools example isn't applicable.
The curvature of spacetime. There are no outward paths for anything that is not moving faster than light, once you are inside the event horizon.
I don't know. I suspect you are thinking of gravity as a force pulling things downward. Relativistic gravity doesn't work that way. It's just the curvature of spacetime is such that light cones "tip over" (scare quotes because this is a coordinate-dependent description) as you approach the event horizon, and all future-directed paths remain below the event horizon.

Yes off course I was considering gravity as a force and not the stretching of spacetime. Sorry! Witch means that to escape it needs to have the escape velocity of more then the speed of light. Thank you!

 

[Sveinbjoern]

You have to distinguish between the universal constant that is the speed of light in a vacuum $c$ (nothing can move faster than that) and the speed of light in a material, which may be less than $c$. If light is influenced by its medium and slows down, that doesn't mean that everything else must be slowed down even more, hence Cherenkov radiation.

In curved spacetime, vectors (including velocity) become a local concept. Which is why we talk about the "local" speed of light: the speed as measured locally.

Yes the curvature is changed by the black hole so that the local speed of light(speed of light in vaccum) has to be overtaken for the object to escape... Thank you!

 

[Orodruin]

Well this is perplexing however that is not a big surprise given the subject matter. If locally light has to be the fastest then how can charenkov radiation exist. Where light moves slower due to being in water and high energy particles travel faster. I guess we are onto what I am not getting. What kind of mechanism are you talking about when you say light has to be the fastest locally?!

Forget about actual light. When we talk about the speed of light we are referring to the speed of light in a vacuum. That is what a black hole event horizon is about. The typical example black hole solution (a Schwarzschild black hole) is a vacuum solution to the Einstein field equations, i.e., there is no matter present at the event horizon.

 

[phinds]

... I simply take the viewpoint of the massive object. It experiences the time dilation ...

This is not correct. NOTHING "experiences" time dilation, which is only something that is seen of it by an observer who is moving relative to it.