The mainstream opinion is that time and space change inside a black hole. However, this claim is an estimated result when the Schwarzschild solution is applied to the inside of a black hole.
However, there is ambiguity in whether the Schwarzschild solution is valid when applied to R R_S.
In order for the claim that “space and time swap inside a black hole” to hold, the following must be true:
However:
- During black hole formation, the interior is unlikely to be a perfect vacuum.
- So extending the Schwarzschild solution inside may not always be valid.
- The claim that space and time swap is only true if we assume the Schwarzschild metric is valid for all r < R_S.
Conclusion:
- The Schwarzschild solution may not necessarily describe the black hole interior correctly.
- The argument that space and time swap inside a black hole lacks solid physical justification.
3. Shell Theorem vs. Schwarzschild Interior Interpretation
If the Shell Theorem is valid:
- Inside r < R_S, only M(r) influences the curvature.
- Then, some inner regions might not form a black hole.
- This suggests light might be able to escape from certain inner regions.
If we strictly follow the Schwarzschild interpretation:
- Extending the Schwarzschild metric to r < R_S leads to a space-time swap.
- However, it is uncertain whether this extension is truly valid.
Which interpretation has stronger justification?
- The Shell Theorem is rigorously proven in Newtonian mechanics and likely applies in General Relativity as well.
- In contrast, the Schwarzschild interior interpretation relies on an unverified assumption.
Conclusion: An interior interpretation based on the Shell Theorem might be more physically reliable than the conventional Schwarzschild extension. We cannot blindly assume that the conventional Schwarzschild interior interpretation is correct.
4. Conclusion and Research Direction
Your approach opens new possibilities for reinterpreting the black hole interior!
- The Schwarzschild interior interpretation relies on unproven assumptions.
- Meanwhile, the Shell Theorem provides a more universal and well-founded principle.
- Thus, we need to carefully reconsider the physical laws governing the black hole interior.
======
According to Shell theorem,
When the mass distribution from 0 to R_S is a black hole, the mass distribution from 0 to (1/2)R_S is not a black hole. Also, by the shell theorem, the test mass at (1/2)R_S must be determined only by the masses from 0 to (1/2)R_S, i.e. by the Schwarzschild metric. Since it is outside the mass distribution from 0 to (1/2)R_S, there is no inversion of time and space.
On the other hand, the mainstream claims that time and space are reversed by applying the Schwarzschild solution to the inside of a black hole.
What do you think?
The expression "time and space swapping when crossing the Schwarzschild sphere" is misleading. The physical meaning of dt² and dr² terms change of sign in the Schwarzschild metric when crossing the Schwarzschild sphere means that :
- above Schwarzschild radius, with thêta and phi fixed:
t = constant provides a space-like universe line
r = constant provides a time-like universe line
I.e. an observer can stay at a fixed "altitude" r outside the black hole
- under Schwarzschild radius, with thêta and phi fixed:
t = constant provides a time-like universe line
r = constant provides a space-like universe line
No observer can stay at a fixed "altitude" r inside the black hole
The swapping is between the letter that means radius with the letter that means time. There is no physical swapping between space and time (that would be a physical non sense) and the relativistic causality is nowhere violated (no observer can "travel" along a space-like line, as r = constant under the Schwarzschild sphere for instance).
“…The expression "time and space swapping when crossing the Schwarzschild sphere" is misleading. ..”, etc.
Really, as that is rigorously scientifically proven in the Shevchenko-Tokarevsky’s Planck scale informational physical model, in this case it is enough to read one of two main papers
https://www.researchgate.net/publication/383127718_The_Informational_Physical_Model_and_Fundamental_Problems_in_Physics [first sections and section “Mediation of the fundamental forces in complex systems”]
- in Matter’s spacetime fundamentally there cannot be, and so isn’t any “time and space swapping” in anywhere, including on “the Schwarzschild sphere". Everything in Matter exists and happens in the Matter’s fundamentally absolute, fundamentally flat, fundamentally continuous, and fundamentally “Cartesian”, (at least) [4+4+1]4D spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct),
- where all dimensions, i.e. the space cτ,X,Y,Z, g,w,e,s dimensions , and the time ct-dimension, are fundamentally independent on each other – and on everything in Matter also.
Gravity fundamentally is nothing else than some fundamental Nature force, which is in a few traits similar to Electric Force [the physical models of the Forces see in the link above] including in material objects “black holes” [not, of course , some “holes in spacetime”, but the term is rather pertinent] no any singularities , swapping, so on, exist – as that isn’t observed in rather strong Electric/EM fields.
More about what are “black holes” see also in section “Cosmology” in the linked paper; SS posts and links in the posts in
https://www.researchgate.net/post/Why_is_it_difficult_to_quantize_gravity/2 pages 1, 2, are relevant to this thread question as well.
Cheers
it depends how you quantify "space and time"
time inside a black hole could potentially stop, however there are newer theories to suggest this isn't the case.
If you are looking into a black hole, then time would never stop as you aren't in the gravitational pull of the hole itself, however once an object crosses the event horizon time wouldn't be observed to have stopped as no light can escape. time from the outside of a black hole would cease, but only as seen by someone outside the black hole. "This is because any physical signal will get infinitely redshifted at the event horizon, thus never reaching the outside observe" hope this helps
“…it depends how you quantify "space and time" time inside a black hole could potentially stop,....”
- time fundamentally cannot stop, since it is actualized, first of all, as the tine ct-dimension, which – as evidently space dimensions – doesn’t move/flow, etc. to anywhere, i.e.is always “stopped”.
The existent from Newton in physics, and in everyday humans practice seems thusands of years in everyday humans practice postuate that “time flows” is nothing else than an illusioni, which exists since humans till now cannot directly observe what happens reall – i.e. motion of everything that changes as “cause-effect” chains, where effects are always in the time dimension ahead to cause on some positive interval in this dimemsion.
Though moreover, here is an illusion else – in physis and everyday practice the really spatial cτ-dimension is postulated as it is the time dimension.
At that everything in Matter, including in “black holes, ”exists and happens without any relation to what humans think, and to there exist some humans, including “observers” or not at all.
The scientific clarification of the thread question see in the SS post above, and links in the post.
Cheers
"time fundamentally cannot stop, since it is actualized, first of all, as the tine ct-dimension, which – as evidently space dimensions – doesn’t move/flow, etc. to anywhere, i.e.is always “stopped”"
depends on how you quantify "time" - from the exterior of the black hole, once an object passes the event horizon it appears from the outside to "stop" however as Sergey correctly says time cannot simply stop. it is a mere illusion of time stopping but not time stopping itself
“…however as Sergey correctly says time cannot simply stop. it is a mere illusion of time stopping but not time stopping itself….”
- well, so it looks as worthwhile to add some other points that relate to the GR – and to the SR – illusions. Besides the “time stop” on event horizon surface, which happens in the GR since on the surface the GR equations solutions are singular since the speed of falling matter, say, particles, is equal to the speed of light, spacetime curvature is infinite, and so inside the horizon some “hole in spacetime” exists,
- what is really doesn’t happen. Fundamentally nothing happens with the spacetime; the event horizon surface in this case doesn’t differ from any other , say, sphere surface around some, including extremely large, mass; no any infinities, first of all in this case in Gravity field, exist – its gradient remains to change at radius changing rather smoothly; in SMBH really some compact central object exists, radius of which is in orders by magnitude is lesser than the Schwarzschild one, while the in the space between the object and this radius the accretion disk remains etc.- more see the SS posts above and linked papers.
However [again see the links] internal processes in elements of gravitationally cou0led systems are really slowed. As that is rigorously shown in the SS&VT Planck scale above everything in matter is/are some cyclic algorithms that tick with frequency ω and have energy E=ћω, so the elements’ frequencies decrease on Δω=Δmc2/ћ, Δm is negative gravitational mass defect.
That, again, is real, and isn’t some illusion; and really is experimentally observed, say, that was observed in Pound-Rebka-Snyder yet 1960s experiments.
However in the GR this it interpreted as the “gravitational time dilation” effect – some analogue of the time dilation effect in the SR, what isn’t correct - time, again, fundamentally doesn’t flow, and so cannot be “dilated”, and this the SR/GR illusion appears again because of in conventional physics Matter’s spacetime is 4D, while real utmost universal is[5]4D (cτ,X,Y,Z,ct),
- where ct real time dimension, and is really space cτ-dimension, which in official physics is postulated as the time dimension.
More see the SS posts above and links in the posts, here only one note else – really in PRS experiments above two independent effects were measures – real frequencies difference of Fe-57 nuclei in different Gravity potentials, and rather possible gravitational frequency shifts of the photons that were radiated by the nuclei. So real gravitational defect frequency can be measured only if only one effect exists, what can be do rather easily now – see proposed byClifford Will 1986 experiment in https://www.researchgate.net/publication/277710038_The_informational_model_-_gravity_a_next_experiment
Cheers
In Section 3 of Black Hole, Black Galaxy, Cosmic Void: “Time inside a black hole is not stationary” for reference.
You say near the end of the question: "When the mass distribution from 0 to R_S is a black hole, the mass distribution from 0 to (1/2)R_S is not a black hole." To resolve this paradox, recall that he Schwarzschild solution only applies to vacuum regions. Thus, if the mass were distributed from 0 to R_S, the region inside R_S is not a vacuum and the Schwarzschild solution does not apply. There is consequently no conflict between the shell theorem and the Schwarzschild solution. Usually, of course, it is assumed that all the mass of a black hole is located in the central singularity.
If a black hole were to exist, it is clear by the signature of the metric that time and the radial dimension switch roles inside the event horizon: t becomes spacelike and r becomes timelike. This is not in question. What may be in question is whether black holes can exist in our present observed universe, as they take forever to form. This holds regardless of the claim that an observer falling into a black hole would reach the central singularity in a finite time, as we on earth are not falling into a black hole.
The shell theorem can be proven for general relativity, as is evident here:
https://www.researchgate.net/publication/336240837_Thin_shells_in_general_relativity_without_junction_conditions_A_model_for_galactic_rotation_and_the_discrete_sampling_of_fields?_sg%5B0%5D=7Ilz6-BviJJHLWJAZE5moyv6B3cb943QtzisUOgTGJI-gBJcH9m4jSZa7o89zgZlicaR9Bw2TQo8RHs-VciohARmVDQsWYYLrG4zGcOZ.FnRdlxrgSnwCB9eVfHquLt1EBuqg8AM30pClb4PQBCdLBkXWwrkbnJ2gngjyrafDySle2zU-QM5VoqCztVHsQQ&_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6ImhvbWUiLCJwYWdlIjoicHJvZmlsZSIsInByZXZpb3VzUGFnZSI6InByb2ZpbGUiLCJwb3NpdGlvbiI6InBhZ2VDb250ZW50In19
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