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I understand that for an outside observer it will take an infinite amount of time for an infalling object to reach the black-hole event horizon.

Consider a black hole that orbits around the center of the galaxy and far from it (far like our sun). There is a non-moving (relative to the galactic center) probe located somewhere on the black-hole's orbit.

Is there a paradox here – the black-hole should hit the probe in a finite amount of time, but on the other hand, it will take an infinite time for the probe to fall (once near) into the black-hole?

Rani Sharoni
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1 Answers1

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Key point of order: the Schwarzschild metric is only valid in the rest frame of the black hole. The coordinate system used would be changed by a shift to any other IFoR, and so would the metric. For this reason also, one cannot say that an object accelerated to sufficiently near the speed of light would become a black hole: the Schwarzschild metric deals with the rest mass of the object in its rest frame.

To consider what would happen to the probe being “hit”, try switching to the black hole’s comoving frame and seeing what the probe’s new trajectory looks like. Whatever happens in that frame is what would be observed, albeit changed by a translation/rotation/boost, by anyone else. Trying to apply the regular Schwarzschild gravitational effects while the BH is moving would result in strange effects.

controlgroup
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