Black holes, speed of light and gravity oh my

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Discussion Overview

The discussion revolves around the relationship between black holes, the speed of light, and gravitational acceleration. Participants explore concepts related to acceleration near black holes, the implications of adding mass to a black hole, and the nature of terminal velocity in the context of relativistic physics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants propose that an object can never reach the speed of light, but can continue to accelerate indefinitely as long as a force is applied.
  • Others argue that the concept of terminal velocity does not apply in the same way in the context of black holes as it does on Earth, where air resistance plays a role.
  • One participant explains that acceleration due to gravity and propulsion are equivalent, suggesting that falling into a black hole does not complicate the process of approaching the speed of light.
  • Another participant highlights that velocities do not add linearly at relativistic speeds, emphasizing that as one approaches the speed of light, the required energy increases nonlinearly.
  • Some participants discuss the implications of adding mass to a black hole, questioning whether this would allow an object to get closer to the speed of light.
  • A participant introduces a comparison to Zeno's paradox, arguing against the idea that one cannot reach the speed of light due to discrete increases in speed.
  • There is mention of the effects of gravitational forces on objects approaching a black hole, with some suggesting that a sufficiently large black hole may not rip objects apart due to a small gravitational gradient.

Areas of Agreement / Disagreement

Participants express differing views on the nature of acceleration and terminal velocity in the context of black holes and relativistic speeds. There is no consensus on the implications of adding mass to a black hole or the interpretation of terminal velocity in this scenario.

Contextual Notes

Some claims rely on specific assumptions about gravitational effects and relativistic physics that remain unresolved. The discussion includes varying interpretations of acceleration and energy requirements at relativistic speeds.

cragar
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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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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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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.
 
As Russ said, a black hole doesn't really have a terminal velocity. The terminal velocity we see on Earth is because of air resistance.
 
our terminal velocity is the speed of light
 
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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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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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
 
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.
 

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