As a proton falls into a black hole, it accelerates. How large will its mass become as it approaches light speed?

1 Answer

Answer :

answer:To answer the title question: The proton will approach light speed as it crosses the event horizon, since that marks the place where light speed is the escape velocity. It won’t quite reach light speed because it has only fallen a finite distance, but it can get arbitrarily close by simply dropping it from a farther distance. As an object reaches light speed, its mass approaches infinity. As to what the observers might see: There are two types of time dilation involved. The first type is that two objects (in this case people with clocks) moving at great speed relative to each other will both observe the other person’s clock tick slower than his own. Person A will think that clock A is faster than clock B, but person B will think that clock B is faster than clock A. As the observers approach c, this effect approaches to each person seeing the other clock stand still in time. The second type is that an object experiencing an accelerating force (such as being close to a black hole) will appear to have a clock that runs slower than an object that is experiencing a smaller accelerating force. An important fact is that both observers agree on which clock is slower. Since there is a whole bunch of time dilation, I’m not quite sure what each person would see. From person B’s point of view (the guy falling into the black hole), the two types of time dilation appear to counteract each other. Since the event horizon marks where the first type approaches infinity (due to approaching the speed of light) but not where there is infinite gravity (that would be the singularity), I think that the first type would be the dominant factor. Person B would see the entire outside universe stand still in time. This might mean that from his own point of view he will never reach the singularity of the black hole. I’m even less sure as to what person A will see.

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