What would be the acceleration due to gravity at the Event Horizon of a Black Hole?

[RobertsMrtn]

TL;DR Summary

The gravitational field of a Black Hole at the Event Horizon would have to be of sufficient strength to prevent light from escaping. The strength of the field would have to be the same for any Black Hole regardless of size. What would be the acceleration due to gravity at this point?

Acceleration due to gravity at the Event Horizon of a Black Hole.

 

[Ibix]

Not a question that makes sense, unfortunately. What Newton would call "the acceleration due to gravity", Einstein would call "the proper acceleration required to hover at constant radius". You can't hover at the event horizon (it isn't even really a place in the ordinary sense of the word - it's an outgoing null surface) so your question is based on an invalid premise.

 

[PeroK]

Summary:: The gravitational field of a Black Hole at the Event Horizon would have to be of sufficient strength to prevent light from escaping. The strength of the field would have to be the same for any Black Hole regardless of size. What would be the acceleration due to gravity at this point?

Acceleration due to gravity at the Event Horizon of a Black Hole.

To expand on what @Ibix said. If an object is falling to Earth, then it experiences no force. An object sitting on the surface of the Earth, however, experiences an upward force from the surface preventing it falling any further. The acceleration due to gravity, therefore, is the acceleration of a falling object in the reference frame of something at rest relative to the surface of the Earth. It's really the proper acceleration of the object on the surface that is being measured!

The same is true when an object falls into a black hole. It experiences no force (except so-called tidal forces). It has no intrinsic or proper acceleration. Its acceleration could be measured by an object at rest relative to the black hole. As one gets closer to the black hole, the force and proper acceleration required to remain at rest relative to the black hole increases without limit. Again, it is that acceleration that is really being measured. And, at the event horizon itself, it is impossible for an object to remain at rest on the horizon, so there is no way to measure an acceleration of an infalling object.

 

[Dale]

As one gets closer to the black hole, the force and proper acceleration required to remain at rest relative to the black hole increases without limit.

I would say that this is the direct answer to @RobertsMrtn’s question.

 

[RobertsMrtn]

Thank you for your reply. According to my calculations, the acceleration would have to be infinite which would require an infinite mass. See my paper here. <personal theory link deleted>

 

[PeterDonis]

the acceleration would have to be infinite

More precisely, the proper acceleration required to maintain a constant altitude above the horizon increases without bound as the altitude goes to zero. Yes, this is well known.

which would require an infinite mass

This, however, is wrong. The above statement about the acceleration is true for any black hole of any finite mass.

See my paper here.

Your paper is not peer-reviewed, and such papers are generally not considered valid references for discussion here at PF. Based on a quick read through of your paper, that policy is certainly justified in this particular case.

 

[PeterDonis]

According to my calculations

Since you evidently did not start this thread to actually get an answer to your question or to understand the correct answer, this thread is closed.