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Would the acceleration due to gravity inside a the event horizon of a black hole theoretically exceed C?

Answer by Frank Heile:

Acceleration has units of meters/sec^2 whereas speeds, such as the speed of light (c), has units of meters/sec. So it doesn’t make any sense to ask if an acceleration exceeds the speed of light - the units do not match.

If you intended to ask whether the speed of an infalling object would appear to exceed c when it falls past the event horizon, the answer is no. The reason it is no is that to measure the speed of an object, you need to indicate the reference frame of the observer who is measuring the speed.

If the observer is someone far from the black hole, or even if they are in orbit around the black hole, they will not measure any speed even approaching the speed of light. In fact as they watch the object fall into the black hole, they will see the object slow down as it approaches the event horizon and actually come to a stop, at the event horizon. The outside observer will never see the object cross the event horizon. The reason for this is that the gravitational time dilation for an object approaches infinity as the object approaches the black hole event horizon when observed by a distant observer.

However, an observer who can observe the object crossing the event horizon would be someone else who is also falling into the black hole - say a few meters behind the first object.  For this infalling observer, both the falling object and the observer will cross the event horizon and will in a finite length of time hit the singularity at the center of the black hole.  However, at no time during this fall into the black hole will the infalling observer ever see the infalling object exceed the speed of light. The further apart the object and observer are, the closer the measured speed might approach the speed of light, but it would never exceed the speed of light.

Confusing and non-intuitive, isn’t it?  Well that is the way it is for special and general relativity.
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