Can Black Holes Accelerate Objects to Light Speed?

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Discussion Overview

The discussion centers around whether a black hole can accelerate objects to the speed of light (c). It explores concepts related to general relativity, the nature of black holes, and the behavior of objects approaching the event horizon.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions if a black hole can accelerate an object to c, noting that its escape velocity exceeds c.
  • Another participant asserts that no object with mass can be accelerated to c, but objects falling into a black hole can approach near light speed relative to an outside observer, depending on the coordinate system used.
  • A participant references the Painleve space-time, suggesting that an observer falling into a Schwarzschild black hole reaches c at the horizon, highlighting a symmetrical aspect of this scenario.
  • It is noted that while the relative velocity between the event horizon and an infalling particle is always c, the particle itself does not actually reach light speed, as its worldline remains timelike, unlike the null worldline of light.
  • A participant expresses gratitude for the clarification regarding the absence of forces or acceleration in general relativity, indicating the complexity of explaining these concepts in simpler terms.
  • Another participant requests a mathematical explanation of the concepts discussed.

Areas of Agreement / Disagreement

Participants express differing views on the nature of acceleration to light speed in the context of black holes, with no consensus reached on the implications of the event horizon and the behavior of infalling objects.

Contextual Notes

The discussion involves complex concepts from general relativity, including the definitions of timelike and null worldlines, and the implications of coordinate systems on perceived velocities. There are unresolved mathematical steps and assumptions regarding the behavior of objects near black holes.

Who May Find This Useful

This discussion may be of interest to those studying general relativity, black hole physics, or anyone curious about the implications of black holes on the nature of speed and acceleration.

cosmic.ash
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can a black hole accelerate an object to c(because its escape v is greater than c)
 
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cosmic.ash said:
can a black hole accelerate an object to c(because its escape v is greater than c)

Nothing with mass can be accelerated to c.

Objects falling into a BH will be accelerated relative to an outside observer to near light speed, however the definition of the actual speed is a local one and will depend on the coordinate system used.

Garth
 
In the Painleve space-time, which is the frame of an observer falling into a Schwarzschild BH from infinity, the velocity of the faller reaches c (wrt to the BH) exactly at the horizon. Which is nice and symmetrical.
 
The good news is that the relative velocity of the event horizon and a particle falling into it when the particle crosses the event horizon is always 'c'.

The bad news is that it is not really correct to think of the particle as being accelerated up to the speed of light. The worldline of the infalling particle is known as "timelike" - this is a characteristic of the worldline of all particles, and is different in nature of the worldline of light, which is "null".

The event horizon is a null worldline (or a collection of them, to be more precise). In fact, you can think of the event horizon as trapped light.

So the worldline of the infalling particle never changes its timelike nature, and the reason that the relative velocity between the event horizon an the infalling particle is equal to 'c' is that the event horizon is lightlike rather than timelike.
 
Pervect, thanks for the clarification. Having no forces or acceleration in GR-speak certainly makes it difficult to explain things in layman's terms.
 
can u explain mathematically
 

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