What happens to the KE of an object as it falls into a black hole?

Question

What happens to the kinetic energy of an object as it falls into a black hole?

Answer 1

Prof Zikzak is right in that KE become fungible depending on your reference point. But I'm not sure if that is the answer you are looking for.

The answer is energy is conserved and E=mc^2

The KE gets added to the mass of the black hole.

Now the tricky part, lets figure out how it occurs:

If you were someplace out in space and dropped an apple which started falling towards a black hole, you would see it gradually pick up speed. But at the same time it is losing potential energy in exactly the same amount as the KE it picks up.

*As an aside, when you get to relativity, KE is measure not by the increase in velocity-squared, but by the increase in mass * c-squared. At our normal low speed world, mv- squared is a good approximation for the change in KE.

As you will recall from special relativity, to you, the outside observer, this increase in speed of the apple will be assiocated with an increase in mass. This increase in mass is exactly equal to the loss of mass from slipping down into the gravitational field. Again E=mc^2.

*Note, if the apple were to suddenly stop its decent towards the black hole, you would preceive it as weighting less by the amount of Potential Energy it lost falling as far as it did. Pretty weird, huh? But the statitonary observer who got hit on the head with the apple would say that it weights the same as when you dropped it, but he would look up at you and say that you weigh more. Even weirder.

So you, as the outside observer watching the decent would see the apple as having the same Energy/Mass all the way through its decent until it hit the event horizon. You would say that all of its KE ended up as increased mass of the black hole.

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As an addition. Both momentum and energy/mass are conserved. The center of mass of the apple-blackhole system stays the same with the black hole subtly shifting towards the apple as it falls.

Answer 2

That's not as easy a question as it seems. In GR, any energy other than gravitational energy of an isolated body is hard to define. Reason: energy depends on the reference frame you measure it in. (You know this. The KE of an airplane is large... if you measure it from the ground. Measured from seat 5A, it's zero.)

In GR, there is no local Lorentz reference frame which contains the entire trajectory of the falling ball (except the ball's own frame), so there is no reference frame in which it's possible to measure KE the whole time (except the ball's frame, in which KE is always zero).

There is a conserved quantity that can be calculated by a distant observer, when he collects all the observations of local observers along the ball's route of flight that reduces to KE in the far field, but now things are getting complicated.

Answer 3

i understand you're talking theoretically, yet an impression with yet another super physique able to adjusting the earth's orbit and sending it in the direction of a supermassive black hollow, could extra advantageous than probable be adequate to end maximum life in the worldwide. If a approach or the different we've been to stay as much as the area of turning into trapped interior of a black hollow's gravity field i could could assume that the layers of Earth could start to peel off long earlier the impression surely handed off. considering that maximum folk stay on the outer layer we would die from the freezing chilly by way of fact the ambience dissipated and all easy could be diverted from the floor. only my concepts.