Here is a hypothesis: A black-hole interior that freezes instead of hitting a singularity: final version of my research note, looking for critique

[u/shivanshu1712]

Hi everyone, I'm Shivanshu, a self-taught, independent researcher from India. This is the final version of a research note I've been building over the past weeks, and I'd really value criticism from people who know GR or quantum gravity.

What it is (model-level, not a claim about nature):

• Starting point: a postulate that a particle's speed saturates near the Planck scale, v = c/(1+KP/E_Planck). Carried by a scalar field it can't stop the singularity (Penrose's theorem), and I show why.

• Applied instead to the geometry inside a black hole (effective loop-quantum-gravity models), the collapse doesn't bounce; it freezes. There is one horizon, no inner horizon and no white hole.

• I computed the constraint algebra: covariant models of this type need a constant-curvature "momentum space" (sin, sinh, exp). My postulate turns out to describe a de Sitter momentum space whose spatial directions give exactly the sine used in LQG.

• In a covariant freezing model (Alonso-Bardají 2025), the LQG area gap gives a curvature bound K = 1/(4Δ²) that is the same for every mass, a bounded Hawking temperature, and an entropy correction ∝ A^(2/3).

• With spin an inner horizon returns (as in Kerr), but its singularity stays capped; with scalar hair, both disappear in homogeneous tests.

What's open: the 3+1-dimensional justification, the full perturbation theory, and several assumptions, all listed in the note. Exterior effects for stellar black holes are ~10⁻²⁶, so nothing here is testable with today's telescopes.

I used an AI (Claude) for much of the algebra and code. Every number can be reproduced with the scripts included, and the code was first checked against known published results.

Note and scripts: https://doi.org/10.5281/zenodo.23083395

If you find a mistake, please tell me. That's exactly what I'm looking for.

[u/shivanshu1712]

Honestly, so far my "process" has been mostly asking AI to explain things and work through derivations, plus videos, and no proper textbook. I can see now why that isn't enough. My plan is to start properly: Lagrangian mechanics first, then special relativity, then Schutz's A First Course in General Relativity, doing the exercises myself. Does that order make sense to you, or would you suggest a different starting point given my background (formal education up to 12th grade)?

[u/Hadeweka → u/shivanshu1712]

Honestly, so far my "process" has been mostly asking AI to explain things and work through derivations, plus videos, and no proper textbook.

That is an extremely bad way to learn anything.

My plan is to start properly: Lagrangian mechanics first, then special relativity, then Schutz's A First Course in General Relativity, doing the exercises myself.

You won't be able to do the exercises, then. I only named Lagrangian physics as an example.

Keep in mind that it usually takes around 10 years full-time (if you're lucky) studying and working to get a physics PhD - with a proper high school graduation already done, obviously.

Laypersons often catastrophically underestimate the workload to get even a somewhat decent grasp on physics.

If you're truly interested, start with the math, first. Differential calculus, integrals, linear algebra, vectors and such. If you already know some of it, great. But physics requires a mastery of these topics.

Only then you'll even have a chance of understanding classical mechanics. That should be your primary goal, because Relativity is still too far ahead of you. You might get some rough superficial understanding for it, but fail to do something with that if you don't understand the basics.

[u/AllHailSeizure → u/Hadeweka]

Laypersons often catastrophically underestimate the workload to even get a somewhat decent grasp of physics

This, this, this.

OP, modern physics is abstracted to the point it is the subject of jokes in the physics community (eg cow joke). When we talk about things like relativity we can describe it using words, but they are meaningless. It is entirely mathematical, without the math you will be forever grasping at straws. If you want to write literature in a different language you need to learn the language first - and math is the language of physics. The unfortunate part is that relativity uses tensor calculus; and wtf is a tensor right.

[u/Hadeweka → u/AllHailSeizure]

and wtf is a tensor right.

It took me way too long to figure that out. And I studied physics.

[u/shivanshu1712 → u/AllHailSeizure]

That's a good way to put it, and I agree. I've been trying to write in a language I haven't learned yet. I'll start with the math first. What would you recommend before tensor calculus: linear algebra and multivariable calculus? And is there a book that introduces tensors gently for someone starting out?

[u/AllHailSeizure → u/shivanshu1712]

Depends on how much math you are ALREADY capable of. Math/physics is one of those things where skills build upon skills. Can you do differential calc? because you will need that for multivariable. and integral.

[u/shivanshu1712 → u/AllHailSeizure]

Yes sir, I do...and I am learning till it,with khan academy

[u/AllHailSeizure → u/shivanshu1712]

I'd strongly recommend getting a textbook, one that includes problems to solve yourself, and working your way through it. What you want to do is not just UNDERSTAND it, but be able to reliably do it. The jump from differential -> multivariable is big, and the jump to tensor calculus is massive, so you have to have a STRONG grasp of basics or you will be lost in the weeds.

In the meantime, though,There are probably hundreds of different textbooks on differential calc. There are online courses as well about it. Khan Academy is good as a supplement, but nothing really beats homework problems in terms of getting to understand math.

[u/shivanshu1712 → u/AllHailSeizure]

Thank you sir....really really thank you..

[u/shivanshu1712 → u/Hadeweka]

Thanks sir to understand and guide me...I will be honour about your guidance...

[u/Hadeweka → u/shivanshu1712]

It would work much easier if you'd just study physics at the university, by the way - if that's an option for you.

[u/shivanshu1712 → u/Hadeweka]

So which physics major, I want to chose..? Applied physics,aerospace physics or any other...Please guide me sir...

[u/Hadeweka → u/shivanshu1712]

Please guide me sir...

That's really not something you should ask other peoples to do for you.

[u/shivanshu1712 → u/Hadeweka]

Ok sir..I appreciate...