What question did this study set out to answer?

This work aims to derive the Kerr metric and predict quasi-normal mode (QNM) frequencies based on the Universal Processing Law framework.

March 26, 2026Open Access

View Full Paper

Universal Processing Law (UPL) — Track 2: Kerr Metric Derivation, Geometric Gradient QNM Prediction, and Development Notes

Key Points

This work aims to derive the Kerr metric and predict quasi-normal mode (QNM) frequencies based on the Universal Processing Law framework.
Document theoretical development of the UPL framework and dual-saturation mechanism.
Derive structural functions of the Kerr metric using boundary conditions.
Analyze 176 gravitational wave merger events from LIGO/Virgo/KAGRA.
Establish QNM frequency shift predictions for Kerr black holes.
Derivation of Kerr metric's structural functions Σ and Δ noted.
Identification of the ergosphere as the activation boundary for the dual-saturation mechanism.
Predicted detectable QNM shifts for near-extremal Kerr black holes at the Einstein Telescope.

Abstract

This upload contains the Track 2 mathematical working documents for the Universal Processing Law (UPL) framework, building upon the foundational UPL preprint (DOI: 10.5281/zenodo.19154977). This record includes four documents: UPL Session Development Notes: Documents the theoretical development trajectory, the DRR dual-saturation mechanism, the Schwarzschild/Kerr complementarity hypothesis, and a pattern analysis of 176 LIGO/Virgo/KAGRA merger events. UPL Track 2 — DRR Tensor Derivation: Formal derivation of the Kerr metric structural functions Σ and Δ from the UPL dual-saturation boundary conditions, with proofs. The ergosphere emerges as the DRR activation boundary. UPL Track 2 — Teukolsky Framework and Geometric Gradient QNM Prediction: Establishes that Φ = Lg·Lv is a geometric functional of the metric, not a Brans-Dicke scalar. Derives a parameter-free structural QNM frequency shift prediction for near-extremal Kerr black holes detectable by the Einstein Telescope. UPL PRL Draft (v2): Complete 4-page Physical Review Letters format manuscript presenting the full Level 2.8 framework for journal submission. All theoretical concepts, derivations, and original ideas are the sole intellectual work of Ahmed Lahmidi. Contact: ahmed.lahmidi.contact@gmail.com

Ask AI

Helpful

Bookmark

View Full Paper

Ask AI

Helpful

Bookmark

View Full Paper

Universal Processing Law (UPL) — Track 2: Kerr Metric Derivation, Geometric Gradient QNM Prediction, and Development Notes

Key Points

Abstract

Cite This Study