Black holes, speed of light and gravity oh my

In summary, the conversation discusses the concept of using a black hole to accelerate an object to near the speed of light. It is explained that while the black hole may add complications, it does not affect the ability to accelerate to the speed of light. It is also clarified that velocities do not add linearly at relativistic speeds and that reaching the speed of light would require infinite energy. The idea of terminal velocity is also discussed and it is explained that it is an asymptote, not a stopping point. It is also mentioned that with a large enough black hole, gravity would not rip a person apart as the gravitational gradient would be small enough.
  • #1
cragar
2,552
3
lets say we had a black hole or something that created a large gravitational field , one that could accelerate something to near the speed of light , so we would have a certain amount of mass or energy that could accelerate our object to near the speed of light as close as we could get it , if we could pack in more mass into this singularity of the black hole so then would this added mass or energy have no effect on accelerating the object because it would be reaching its terminal velocity . or would this be like the amount of energy in the universe .
 
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  • #2
That's one long and incoherent sentence but maybe this helps: an object can never reach the speed of light but as long as you keep applying a force it will keep accelerating. There is no terminal velocity like you are describing.
 
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  • #3
how can you keep accelerating something and yet it will never reach the speed of light ,
and how could it not reach a terminal velocity.
 
  • #4
As Russ said, a black hole doesn't really have a terminal velocity. The terminal velocity we see on Earth is because of air resistence.
 
  • #5
our terminal velocity is the speed of light
 
  • #6
OK, let's clear a few things up:

1] Acceleration due to gravity and acceleration due to propulsion are synonymous. Whether you accelerate by using your engines or you accelerate by falling into a black hole has no effect on how close to the speed of light you can get. All I'm trying to say here is: the BH does not add a complication to accelerating to c.

2] Velocities do not add linearly at relativistic speeds. If you are traveling at .9c and you (either turn on your engines or fall into a BH), you will not "hit" 1.0c. What happens is your velocity goes from .9c to .99c. If you continue to accelerate, your velocity will reach .999c. You can accelerate until you grow old, and your velocity will reach .999999999c.

The formula is [tex]v = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}[/tex]


So, c is not a terminal; it is an asymptote.
 
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  • #7
cragar said:
how can you keep accelerating something and yet it will never reach the speed of light ,
and how could it not reach a terminal velocity.

Suppose you are traveling atr very nearly the speed of light; only 2kph slower. You can apply an acceleration force, and cover 1/2 the difference. Now, you are just 1kph slower than c. Apply more acceleration, and oyu make up half the difference again; you are now traveling c-.5kph. You can keep accelerating through c-1/4, 1/8,etc...

you continue to accelerate, but never reach c. And so, no lightspeed and no terminal velocity.

EDIT:
Or, y'know... what Dave said.
 
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  • #8
If you go from a velocity of β=0.999 to β=0.9995, the γ goes from about 22 to 32; i,e, the energy increases by ~45%. It is very nonlinear in the amount of energy required.
Bob S
 
  • #9
ok i think i understand, so if i kept adding mass to the black hole i would just keep getting closer to the speed of light .
 
  • #10
LURCH said:
Suppose you are traveling atr very nearly the speed of light; only 2kph slower. You can apply an acceleration force, and cover 1/2 the difference. Now, you are just 1kph slower than c. Apply more acceleration, and oyu make up half the difference again; you are now traveling c[/ki]-.5kph. You can keep accelerating through c-1/4, 1/8,etc...

you continue to accelerate, but never reach c. And so, no lightspeed and no terminal velocity.


Forgive me if I'm misunderstanding, but I'm not sure this is quite right. The above is a statement of Zeno's paradox. It's the classic paradox involving a man standing near a wall. To reach the wall he must first cross half the distance, and then half that distance, ad infinitum. Thus he can never reach the wall. The fallacy can only be exposed by the mathematical notion of functional continuity; motion is continuous, and shouldn't be discretized as the paradox describes.

Here we're dealing with velocities, but the idea is the same. Velocity is continuous, so discretized increases in speed isn't the reason we can't reach light speed. The reason is because the relativistic energy is proportional to the gamma factor, and as speed increases, the gamma factor goes to infinity. Thus it would require infinite energy to accelerate any massive object to c.

Again, sorry if I'm misunderstanding what you said.
 
  • #11
cragar said:
ok i think i understand, so if i kept adding mass to the black hole i would just keep getting closer to the speed of light .

"You" would never get anywhere in the vicinity of c, though what is left of you after gravity has ripped you to pieces will be accelerated to greater speeds for greater mass black holes. Exactly what speed you reach at a certain radial distance from the BH depends on where you started from.
 
  • #12
DaveC426913 said:
So, c is not a terminal; it is an asymptote.

To be fair, a terminal velocity as created by air resistance is also an asymptote.
 
  • #13
Nabeshin said:
To be fair, a terminal velocity as created by air resistance is also an asymptote.

Yes, I didn't mean to imply it wasn't. I was trying to disabuse the OP of the notion that, wrt reaching c, acceleration increased until some point, as then just stopped.
 
  • #14
espen180 said:
...what is left of you after gravity has ripped you to pieces...

With a large enough black hole, the gradient is small enough that gravity will not pull you apart.
 
  • #15
espen180 said:
"You" would never get anywhere in the vicinity of c, though what is left of you after gravity has ripped you to pieces will be accelerated to greater speeds for greater mass black holes. Exactly what speed you reach at a certain radial distance from the BH depends on where you started from.

I did an elaboration on the speeds of infalling observers from infinity which might be useful for this discussion in a thread not too long ago. I might think about an analysis for observers infalling from a given radius later, or someone else could do that:
https://www.physicsforums.com/showpost.php?p=2476880&postcount=6
https://www.physicsforums.com/showpost.php?p=2477762&postcount=12

(First post included because the second isn't very self-contained).
 
  • #16
thanks for your answers guys , you put a lot of effort into them.
 

1. What exactly is a black hole?

A black hole is a region in space where the gravitational pull is so strong that nothing, including light, can escape from it. It is formed when a massive star dies and collapses under its own gravity, becoming incredibly dense.

2. How fast is the speed of light?

The speed of light is approximately 299,792,458 meters per second, or about 670 million miles per hour. This is the fastest speed at which anything can travel in the universe.

3. What is the relationship between black holes and gravity?

Black holes have an incredibly strong gravitational pull due to their immense mass and density. This pull is so strong that it can even affect the motion of nearby objects and distort space-time.

4. Can anything escape from a black hole?

No, nothing can escape from a black hole once it crosses its event horizon, which is the point of no return. This includes light and even matter.

5. How do scientists study black holes?

Scientists use various methods to study black holes, including observing their effects on surrounding matter and using telescopes to detect the radiation emitted from the matter as it falls into the black hole. They also use mathematical models and simulations to better understand the behavior of black holes.

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