Event Horizon Gravity: Infinite or Not?

[Mike Holland]

In my browsing around various science forums a have come across the comment that the gravity field becomes infinite at the event horizon. I have always thought that this is a misunderstanding, and that it only becomes infinite at the central singularity. Then I found this same statement in Novikov's book 'Evolution of the Universe'. Is this correct?

For a falling body, time dilation becomes infinite at the event horizon, so if gravity does too, we have an irresistible force meeting an immovable object , an old philosophical conundrum. Logic says these cannot both exist in the same universe. But the two effects may not approach infinity at the same rate, and this would affect the outcome. I would put my money on Time Dilation coming out tops, because I have this obsession that nothing happens when time stops.

 

[PeroK]

In my browsing around various science forums a have come across the comment that the gravity field becomes infinite at the event horizon. I have always thought that this is a misunderstanding, and that it only becomes infinite at the central singularity. Then I found this same statement in Novikov's book 'Evolution of the Universe'. Is this correct?

For a falling body, time dilation becomes infinite at the event horizon, so if gravity does too, we have an irresistible force meeting an immovable object , an old philosophical conundrum. Logic says these cannot both exist in the same universe. But the two effects may not approach infinity at the same rate, and this would affect the outcome. I would put my money on Time Dilation coming out tops, because I have this obsession that nothing happens when time stops.

The event horizon is not a physical singularity. It is a coordinate singularity in Schwartzschild coordinates. In the same way that the North pole is a coordinate singularity in spherical coordinates.

A falling body would pass through the event horizon - time dilation is only relative to a distant observer. To the infalling body time passes normally and, in particular, the event horizon is crossed aftre a finite time, according to the infalling object's clock.

 

[Orodruin]

If you want to know how GR works, you need to learn actual GR rather than base reasoning on popular science.

 

[Vanadium 50]

If you want to know how GR works, you need to learn actual GR rather than base reasoning on popular science.

True, but the OP has been receiving this advice for years, and yet here we are.

In my browsing around various science forums

You've been here long enough to know this is not an acceptable reference. How can we check what they are actually writing?

the gravity field becomes infinite at the event horizon.

This mixes Newtonian and relativistic concepts in such a confusing way as to be meaningless. (But will surely start the usual long and pointless PF thread called "guess what the author of the nonsensical statement must have really meant") But even in the classical Laplacian black hole, this is not a correct statement.

because I have this obsession

The universe is not obliged to arrange itself according to your obsessions, though.

 

[pervect]

In my browsing around various science forums a have come across the comment that the gravity field becomes infinite at the event horizon. I have always thought that this is a misunderstanding, and that it only becomes infinite at the central singularity. Then I found this same statement in Novikov's book 'Evolution of the Universe'. Is this correct?

For a falling body, time dilation becomes infinite at the event horizon, so if gravity does too, we have an irresistible force meeting an immovable object , an old philosophical conundrum. Logic says these cannot both exist in the same universe. But the two effects may not approach infinity at the same rate, and this would affect the outcome. I would put my money on Time Dilation coming out tops, because I have this obsession that nothing happens when time stops.

Good news. The behavior of bodies at the event horizon can be computed with quantities that are finite and well-behaved.

Bad news. The quantities you insist on using, your particular notion of "gravity", and for that matter, time dilation, are not such quantities. So, any approach that insists on using these quantites must run into the dificuties that you have already noticed. The basic solution is simple - use different quantities, that are well behaved. But understanding these quntites and their relationship to what one can observe and the mental framework that one uses to analyze them is not a trivial undertaking.

There are many general approaches one might take to understand gravity, and black holes. While I'm rather fond of Baez's "The meaning of Einstein's equation", https://arxiv.org/pdf/gr-qc/0103044.pdf, it might not be the best choice for you, however.

Additionally, with almost any approach, you're going to run into the difficulty of missing background. For instance, in Baez's paper above, he writes:

Before stating Einstein’s equation, we need a little preparation. We assume the reader is somewhat familiar with special relativity — otherwise general relativitywill be too hard.

It's worth reading some of the following statements Baez makes, about the nature of velocities in general relativity. If they seem confusing, it's a sign of some missing background. Baez tries hard, but I think he does use some background from manifolds and differential geometry that is probably not familiar to the reader that he doesn't mention, as well as more specific issues revolving around the need to understand special realtivity first, before attempting to tackle general relativity.

That's getting a bit off-topic, though. The main point is that by insisting on trying to understand things in terms of things that are not finite, you are dooming your effort to understand GR, no matter how attractive comfortable, familiar, and useful those familiar notions of "gravity" and "time dilation" seem to you.

 

[PeterDonis]

In my browsing around various science forums

Which are not valid sources; you need to look at textbooks and peer-reviewed papers.

the gravity field becomes infinite at the event horizon

"Gravity field" is an ambiguous term, but no physically meaningful quantities are infinite at the horizon, so whatever "gravity field" means in this context, it isn't a physically meaningful quantity at the horizon. (The most likely meaning is "proper acceleration of a stationary observer", and there are no stationary observers at the horizon.)

Then I found this same statement in Novikov's book 'Evolution of the Universe'.

He probably means it in the sense I just gave (proper acceleration of a stationary observer), in which case it's the sort of misstatement that is (unfortunately) typical in pop science books.

For a falling body, time dilation becomes infinite at the event horizon

No, "gravitational time dilation" is not well-defined at the horizon, since it is only well-defined in a region where there are stationary observers, and there are no stationary observers at (or below) the horizon. So it is not physically meaningful at the horizon for the same reason that "gravity field" in the sense I described above is not.

we have an irresistible force meeting an immovable object , an old philosophical conundrum

No, we just have a failure on your part to recognize the limitations of the concepts you are trying to use.

 

[PeterDonis]

The OP question has been answered. Thread closed.