Prototype

Timelike Geodesic Solver

A planned numerical notebook surface for tracing timelike paths through selected spacetime models.

g_{\mu\nu}

What the tool does

The solver will define initial conditions, integrate geodesic equations, and record the numerical settings needed to reproduce each trajectory.

Why it matters

Geodesic tracing makes causal claims more concrete by showing how local metric structure shapes possible timelike motion under stated assumptions.

Connection to CTC paper

Yuvan's paper discusses geodesic tracing as part of a broader computational workflow for studying closed timelike curves and embedded spacetime geometry.

Research role

The page will prioritize clear initial data, numerical tolerances, and references to the metric definition used for each run.

Near-term build

A reliable first milestone is a small gallery of precomputed trajectories with solver metadata, followed by controlled interactive experiments.

Sanity Check Artifact

Prototype solver validation checks

This artifact documents the minimum checks required before the prototype geodesic solver publishes numerical trajectories. It defines validation expectations for a future solver implementation; it does not claim production readiness or report completed numerical results.

Geodesic equation

\frac{d^2x^{\mu}}{d\lambda^2}+\Gamma^{\mu}_{\alpha\beta}\frac{dx^{\alpha}}{d\lambda}\frac{dx^{\beta}}{d\lambda}=0

Prototype validation checklist

Flat spacetime baseline

In Minkowski spacetime, the solver should recover straight-line motion in inertial coordinates before curved-spacetime examples are trusted.

Conserved quantities

Where Killing symmetries exist, conserved quantities should remain stable within stated numerical tolerances.

Step-size sensitivity

The same initial data should be run at multiple step sizes so qualitative path behavior is not tied to one discretization choice.

Timelike/null normalization

g_{\mu\nu}u^{\mu}u^{\nu}=\mathrm{constant}

The solver should monitor the normalization of the tangent vector under the chosen metric and convention.

Trajectory language

Visual paths should be described as trajectories under stated assumptions, not as proof of global causality.

Reproducibility artifact

The public artifact records the planned checks for a future geodesic solver. It intentionally does not publish numerical trajectories or claim production solver status.

Open sanity-check artifact

Research caution

Prototype only. Numerical trajectories are research-support artifacts and should not be presented as physical conclusions without convergence checks and analytic comparison.