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Can there be a black hole large enough to pull objects faster than light


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I was watching this Documentary on Google Videos on SuperMassive Black Holes and they where saying that they have enought Gravitational Pull to make a Nearby Planet or Star Orbit faster than Light or near.

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If the speed of light has a finite speed why would you need infinite acceleration?

 

Because as things go faster you need more energy to increase their speed by the same amount. This goes up quite quickly and for a finite mass at c it takes infinite energy.

 

This drops out of relativity.

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If the speed of light has a finite speed why would you need infinite acceleration?

You wouldn´t. Any non-zero constant acceleration applied for a sufficient amount of time would do, for example. However, as Klaynos mentioned, the energy required to reach a velocity arbitrary close to c is a limiting parameter here. Technically, this will show in that you simply cannot have an acceleration profile that will result in v>c.

Example: If you accelerate a mass m with a constant force F, the acceleration is given by [math] a = \sqrt{1-v^2 / c^2} \, F / m [/math] and goes towards zero as v approaches c (also note that if v<<c, then a = F/m as you know it from Newtonian Mechanics).

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You wouldn´t. Any non-zero constant acceleration applied for a sufficient amount of time would do, for example. However, as Klaynos mentioned, the energy required to reach a velocity arbitrary close to c is a limiting parameter here. Technically, this will show in that you simply cannot have an acceleration profile that will result in v>c.

Example: If you accelerate a mass m with a constant force F, the acceleration is given by [math] a = \sqrt{1-v^2 / c^2} \, F / m [/math] and goes towards zero as v approaches c (also note that if v<<c, then a = F/m as you know it from Newtonian Mechanics).

 

Depends on your reference frame. From my point of view, my acceleration from a constant force is constant. I just never actually get any closer to C.

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My statement was frame-independent in the sense that it applies in any frame of reference. The constant acceleration an object has in its own frame of reference comes from the force F=0 it experiences in its own frame of reference. Note that F, a and v are three-vectors; they are not invariant under transformations, meaning they can be zero in one frame but non-zero in another.

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