Scientific Computing · General Relativity

5D Manifold
Solver_

An installable, tested Python package that computes the curvature of a five-dimensional Schwarzschild-Verhave metric — deriving the Einstein tensor analytically and mapping the transition from a shell to a regular black hole.

View code 📄 Read the preprint
Python NumPy pytest GitHub Actions CI Packaged (pip-installable) Cosmology (v0.2.0)
manifold.solver — output ~/5d-etheric-manifold
Five-dimensional Schwarzschild-Verhave metric curvature visualization

Overview

This packages my computational general-relativity work into a clean, reproducible repository. It numerically and analytically studies a five-dimensional, two-time ("Schwarzschild-Verhave") metric: it computes the Einstein tensor in closed form and maps the shell→regular-black-hole transition at the critical coupling αc = rs²⁄4. It's a portfolio piece that shows I can take exploratory research scripts and turn them into tested, installable, CI-backed software.

Highlights

∑ Analytic Einstein tensor

Curvature is derived in closed form rather than purely numerically, then cross-checked against numerical evaluation.

🕳️ Regular black-hole mapping

Locates the critical coupling where a singular shell becomes a regular (singularity-free) black hole.

✅ Tested

17 passing pytest checks: Bianchi identity, Schwarzschild limit, vacuum solution, grid convergence — plus the cosmology suite (de Sitter horizon, supernova fit, quintessence).

📦 Engineered, not scripted

Refactored a real side-effect bug (import-time plotting) into clean solver / figures modules with a CI workflow and a v0.1.0 release.

Update v0.2.0 — Dark energy & cosmology

The same Schwarzschild-Verhave machinery, extended into a cosmological setting: a new manifold.cosmology module (pure NumPy) that studies dark energy three ways. The middle one bridges straight back to the black hole — adding a cosmological constant term −Λr²⁄3 to this metric's own lapse f(r) wraps a de Sitter horizon around the regular black hole at r ≈ √(3⁄Λ). Eleven new physics tests bring the suite to 17 passing.

cosmo-lcdm.png
LCDM expansion history, deceleration parameter, and a supernova Hubble diagram
ΛCDM expansion: gravity decelerates the universe, then dark energy switches acceleration on at z ≈ 0.63. A mock Type-Ia-supernova fit recovers ΩΛ ≈ 0.7 and rules out a matter-only universe by Δχ² ≈ 217 — the shape of the 1998 accelerating-universe discovery.
cosmo-lambda.png
The 5D lapse f(r) gaining a de Sitter horizon as Lambda increases
Dark energy in this metric: with Λ = 0 the regular black hole is horizonless, but switching on a cosmological constant makes a de Sitter (cosmological) horizon appear near √(3⁄Λ) — Schwarzschild–de Sitter structure.
cosmo-quintessence.png
Quintessence dynamical equation of state and the matter to dark-energy crossover
Quintessence: dark energy as a rolling scalar field. Its equation of state w(a) starts frozen at −1 (like a constant Λ) then rises to ≈ −0.93 today — dynamical, not constant — as the field comes to dominate. That field is the cosmological cousin of the scalar gradient Φ′ the solver already reconstructs.
Standard flat-FRW physics. The ΛCDM and de Sitter horizon results are exact; the supernova fit uses mock data (demonstrating the method, self-consistently); the quintessence potential is illustrative, chosen for a clean demo rather than fit to data.

From notebook to package

Part of a wider body of speculative-physics manuscripts (5D manifolds, dual temporal manifolds, quantum-consciousness models) — this repo is the one engineered to professional, testable standards.