Can there be a maximum curvature of spacetime?

[HansH]

TL;DR

we know that in our universe nothing can go faster than c. accordng to Einstein curvature related to a dense object such as black hole can become so large that according to the waterfall model we get an event horizon because that is the border where the fallling waterfall exceeds the speed of light. how do we know that this is correct and not limited to c also?

The waterfall model is used in several places such as

https://jila.colorado.edu/~ajsh/insidebh/waterfall.html
how do we know so sure that the speed of the falling in arrows (wheatver that may be) can exceed the speed of light while on the other hand we assue the speed of light is the speed of causality?
I assume we cannot define experiments that can confirm this because we can never create the circumstances on earth. So could it be possible that actually this is not what happens but instead curvature of spacetime is limited due to the fact that there cannot be any effect having a speed larger than the speed of causality?
The result would be dramatically different from our theory so far as it would mean that we don't have event horizons and also no singulatities because then only this maximum of c can be reached at the limit reaching the mass that causes the curvature.

So my question is if there is evidence for this part of general relativity preventing it from being different from as we think it is? (such as contradictions proving that this alternative cannot be the case?) so can be prove that the 'double relativity' efect in the second picture cannot be the case?

see pictures to show the idea:
first picture shows the effect of relativity causing the speed due to constant acelleration not to exceed c

second picture shows the idea of a second relativistic effect causing the general relativity to be limited by a second higher level relativity (I call that 'double relativity') that limits the curvature of spacetime to a maximum similar to limiting the speed to c at relativity compared to infinite at
traditional theory

 

[HansH]

'tijd' = 'time' in the first picture (sorry it was tanslated from Dutch)

 

[jbriggs444]

Trying to reason from popular science concepts such as the water fall analogy will not lead you to a correct understanding. You need to work from a textbook.

"Curvature" of space time is a locally defined quantity, e.g. the Riemann curvature tensor. Unlike the curvature of a two-dimensional space (which can be modelled as a simple scalar), the curvature of a four dimensional space is a tensor. Tidal forces scale with the Riemann curvature tensor.

The curvature at the event horizon of a black hole depends on the size of the hole. For a large hole, the local curvature at the event horizon can be small. For a small hole, the local curvature at the horizon can be large so that spaghettification is a concern.

Although we have no way to directly measure the space time curvature inside of an event horizon, we confidently predict that general relativity continues to apply inside, just as it does outside. The prediction is that curvature increases as the singularity is approached and that it increases without bound.

There is reason to doubt that general relativity applies in the limit as the singularity is approached.

 

[Ibix]

Nothing goes faster than light in Schwarzschild spacetime in the relevant sense that nothing can overtake a light pulse. So no modification is needed.

Some choices of coordinates can give you arbitrarily high coordinate speeds, but that's unimportant. Naive application of Schwarzschild coordinates can also be misleading because the functional form of the timelike coordinate's metric component inside the hole is the same as the radial metric component outside the hole and vice versa. Careless calculation that assumes that something is a time just because it's labelled $t$ can also cause misunderstandings.

As @jbriggs444 notes, it's a bad idea to try to learn pjysics from popularisations. Carroll's GR notes are freely available online and teach the actual theory.

 

[Nik_2213]

And then there's this...

Physicists suggest tachyons can be reconciled with the special theory of relativity​

https://phys.org/news/2024-07-physicists-tachyons-special-theory.html
whimsy:
Could such nimble, if hypothetical beasties freely escape from any gravitational singularity ?
Or 'only' from a zone just within the 'Event Horizon' ??
/

 

[HansH]

Trying to reason from popular science concepts such as the water fall analogy

from https://jila.colorado.edu/~ajsh/insidebh/waterfall.html I understand that this is not simply a popular science concepts as it says:

"The picture of spacing falling into a black hole has a sound mathematical basis, first discovered in 1921 by the Nobel prize-winner Alvar Gullstrand2, and independently by the French mathematician and politician Paul Painlevé3, who was Prime Minister of France in 1917 and then again in 1925.
It is not necessary to understand the mathematics, but I do want to emphasize that, because the concept of space falling into a black hole is mathematically correct4, inferences drawn from that concept are correct."

so is that conclusion then wrong?

 

[HansH]

The curvature at the event horizon of a black hole depends on the size of the hole. For a large hole, the local curvature at the event horizon can be small. For a small hole, the local curvature at the horizon can be large so that spaghettification is a concern.

So the curvature at the event horizon is not what defines the conditions for an event horizon to occur. not sure why you use this fact in your answer in relation to my question.

 

[PeterDonis]

second picture

Is your personal speculation, which is off limits here. You have received a number of good responses that describe what relativity says.

 

[Dale]

according to the waterfall model we get an event horizon because that is the border where the fallling waterfall exceeds the speed of light. how do we know that this is correct and not limited to c also?

Sounds like a good reason to abandon the waterfall model and use GR without an unnecessary add on.

By the way, the speed of the waterfall is unrelated to the local curvature.

 

[PeterDonis]

Since the OP question is based on personal speculation, this thread is now closed.