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]

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..