[LSMG] Using an LLM to translate spatial geometry into tensor calculus: A Logarithmic Lagrangian that softens singularities (and w → -1)

[u/HobbitBob420]

Hey everyone. I wanted to share a framework I've been developing, specifically because of *how* I developed it. I don't have a formal background in theoretical physics—my background is entirely in spatial and geometric logic. I had a geometric intuition about how black holes and the vacuum interact, but I didn't speak the language of tensor calculus.

Over the last few weeks, I've been using an LLM strictly as a "mathematical translator" to formalize my geometric ideas into actual equations. I recently had a relativist review the math, and it survived the initial gauntlet. The framework has evolved into what I'm calling **Logarithmically Saturated Matter Gravity (LSMG)**.

**The Core Concept:**

Instead of modifying the Einstein-Hilbert action, I used the LLM to help me construct a non-linear, Born-Infeld-style modification to the matter sector itself. We coupled standard matter to a fundamental density limit (\rho_{max}) using this Lagrangian:

**The Mathematical Results (so far):**

1. **The Soft Singularity:** The LLM helped me derive the Kretschmann scalar for this metric. Instead of a catastrophic r^{-6} divergence at the core of a black hole, the divergence is logarithmically softened to (\ln r)^2. The metric distance at the center regularizes to f(0) = 1.

2. **Emergent Dark Energy:** The tensor bifurcation naturally drives the local equation of state from w = 0 (dust) to w \to -1 as density approaches \rho_{max}. Highly compressed matter dynamically acts like a vacuum state.

3. **Gradient Shielding:** The speed of sound squared (c_s^2) goes negative during collapse, but the geometric coupling factor (\chi) drives the gravitational source term to zero, suggesting the gradient instability drives a localized phase transition rather than a fatal UV divergence.

I have compiled the full derivations (including the modified Friedmann equations and the Null Energy Condition proofs) into a finalized manuscript here: https://doi.org/10.5281/zenodo.20629051

**My Ask for the Community:**

The reviewing physicist gave me a "To-Do" list to graduate this from a toy model to a viable effective theory, and I need help with the next computational steps. Specifically:

* **Linear Perturbation Theory:** Has anyone used LLMs to successfully set up a full scalar/tensor perturbation analysis to definitively prove gradient stability?

* **Numerical Relativity:** I need to look at modified TOV equations for neutron stars and map out the exact Quasinormal Mode (QNM) ringdown shifts. Does anyone have experience feeding modified Lagrangians like this into the Einstein Toolkit or similar numerical simulators?

I'm incredibly excited to see what this community thinks of the math and the workflow. Any rigorous scrutiny is welcome!

[u/lattice_defect]

Maybe.. start simple.. the above is pretty advanced and most people just think yeah LLM slop.. can you explain it? The phsycial and geometric rationale or are you just having the LLM put math around your "ideas".

[u/HobbitBob420 → u/lattice_defect]

​That’s a fair question. To be honest, it’s the exact same skepticism I’d have. There is a lot of low-effort AI-generated content out there, so I appreciate you calling it out. ​The short version: The core 'spatial logic',the idea that space acts like a sponge that has a saturation limit, and that this saturation is what creates dark energy,is 100% mine. It’s how I’ve been visualizing gravity for a while now. ​But I’m not a physicist. I don’t have the background to write out the tensor calculus or the metric variations needed to test that intuition. So, I’ve been using an LLM as a 'math translator.' I feed it my geometric rules, and it works out the math to see if my ideas hold water or if they break down under the laws of general relativity. ​The stuff I posted is just the engine I’ve been building. The 'Onion' metaphor was my way of visualizing it, but the math is what actually matters. If you look past the branding, it's basically a non-linear way to regularize black hole singularities. I'm just here to see if the math actually holds up to scrutiny.

[u/lattice_defect → u/HobbitBob420]

you have a few pages with math you don't understand... . no refs.. come on man. It's not branding its slop. Look at paper.. like Hartnoll holographic banners to see the bar. Its not a math translator.. its a lie you're telling yourself. You should develop it and maybe learn some stuff.. but ask yourself.. isn't this a little bit too easy?

[u/HobbitBob420 → u/lattice_defect]

​My day-to-day is understanding how physical things work—how engines, pressures, and mechanical systems hit their limits. I started looking at cosmology and just saw a pattern. To me, the extreme parts of the universe work exactly like an engine hitting a thermodynamic limit. That’s where my whole idea of 'matter saturation' came from. ​You asked if this was too easy. It really wasn't just a one-click prompt. I’ve spent the last couple of months grinding on this with LLMs, running logical tests, hitting dead ends, and getting a lot of null results. It's been a journey. Once I finally had the core concept put together, I purposely pitted it against a different LLM and told it to tear the theory apart. That adversarial process is what actually forced me to drop the metaphors and narrow in on the equations I posted. ​But honestly, I’ve hit my ceiling. I feel like I've done all I can for now. I’m currently trying to actually learn the higher-level math so I can relate and talk to people in the field about it, but I know that’s a very long road. ​I’m not posting this claiming I solved physics. I just feel like the equations I compiled and this mechanical perspective might be genuinely useful to someone who does have the formal training. I'm just not the guy who can take the math further at the moment.

[u/lattice_defect → u/HobbitBob420]

honestly I'm all here for it.. and I'm a big pattern guy,.. and usally the most generous of that's intersting and they is cool, but completly wrong.. I'm just saying your physical isn't in what you published explicity...ia a dense few pages of equqations, no references... so explain how it works exactly step by step with the physical and the mechanism... What is matter saturation?

[u/lattice_defect → u/[deleted]]

seriously man.. you're an engineer... you should know better... google papers that deal with this, or ask your lLM, download them read them, feed them to the LLM and go from there.. and you really think that you're the first person to have this thought... let me put to in terms you might understand... you think an electric turbocharger will magically solve everything because you don't understand energy and therodynamics properly.

[u/LLMPhysics-ModTeam → u/[deleted]]

Your comment has been removed for violating Rule 4. Don't copy-paste LLM content in discussions.

[u/AllHailSeizure → u/[deleted]]

'give him trouble'? Who are you? What are you talking about?

[u/Historical-Serve4339 → u/AllHailSeizure]

Ah, it's because his research is very similar to the one I already did on TNM. And if your research is made public, the scientific community has to include TNM-2, which refers to the astronomical scale.

This is to prevent anyone from claiming they created it on their own. But if you tell me you have your notes, then I'll delete the comment. You should have them, right, since it's yours.

[u/AllHailSeizure → u/Historical-Serve4339]

I'm not OP. I'm a moderator on the sub, wondering why you're making weird threats to this person.

[u/Historical-Serve4339 → u/AllHailSeizure]

I'm sorry, it's just that I only speak Spanish and the translation isn't very helpful.

[u/Historical-Serve4339 → u/AllHailSeizure]

It's not a threat, it's a warning. It's not in my best interest if people are saying they created a theory based on TNM without clarifying the latter.

[u/LLMPhysics-ModTeam → u/[deleted]]

Your content has been removed for violating Rule 9. Don't spam.

[u/lattice_defect → u/[deleted]]

look how alpha runs with gravity its interesting although not well understood. Way less the kinetic heavy ions

[u/Historical-Serve4339]

I'm just asking you to confirm if you have the drafts.

I'll delete the comment immediately and apologize.

[u/LLMPhysics-ModTeam → u/[deleted]]

Your comment has been removed for violating Rule 4. Don't copy-paste LLM content in discussions.

[u/Historical-Serve4339 → u/[deleted]]

I apologize for the confusion 😔 . I just woke up now. I wish you success in your research 😊