Public Research Tools

Computational Relativity Lab

A public-facing workspace for reproducible general relativity calculations, causal-structure visualizations, and validation records connected to Yuvan Raam Chandra's investigation of closed timelike curves.

These tools are educational and research-support prototypes. They are designed to make assumptions, equations, and computational checks visible; they do not claim new physical results unless a result is explicitly validated and cited.

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Metric → Tensor Calculator

A planned metric-first workflow for deriving geometric tensors from a specified spacetime line element.

G_{\mu\nu}

What it does

The calculator is intended to accept a metric ansatz, organize the components, and expose intermediate steps toward Christoffel symbols, curvature tensors, and Einstein tensor terms.

Why it matters

For general relativity work, a reproducible tensor pipeline reduces transcription errors and makes it easier to audit each symbolic step before interpreting a physical result.

CTC paper link: Yuvan's CTC paper depends on tracing how metric choices affect causal structure and energy-condition checks. This tool frames those calculations around the metric components and the tensor quantities they generate.

Validated demo

Gödel CTC Visualizer

A visualization page for the causal transition in Gödel spacetime and the emergence of azimuthal closed timelike curves.

g_{\phi\phi} < 0

What it does

The visualizer will present the critical-radius idea, show where circular paths change causal character, and connect plotted regions to the sign of the angular metric component.

Why it matters

Visual representations help separate coordinate facts from physical interpretation, especially when studying causality violations in exact solutions.

CTC paper link: The CTC paper uses Gödel spacetime as a central example for chronology violation. This tool turns the paper's causal-radius discussion into a reproducible visual reference.

Prototype

Timelike Geodesic Solver

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

g_{\mu\nu}

What it 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.

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

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Validation Archive

A central public record for assumptions, benchmark checks, pending artifacts, and publication standards behind the lab's computational relativity work.

r_c = \ln(1 + \sqrt{2})

What it does

The archive will collect derivation checks, symbolic-computation comparisons, numerical tolerances, references, and known limitations for the lab's computational relativity work.

Why it matters

Validation records are essential for reproducibility. They make it clear which outputs are trusted, which remain exploratory, and which require further review.

CTC paper link: The CTC paper benefits from an explicit audit trail for tensor calculations, causal thresholds, energy-condition statements, and visualization choices.

Validation posture

The lab is intentionally conservative: symbolic expressions such as $g_{\\mu\\nu}$ and $G_{\\mu\\nu}$ should remain attached to coordinate conventions, derivation steps, and benchmark comparisons. The Gödel threshold discussion, including $g_{\\phi\\phi} < 0$ and $r_c = \\ln(1 + \\sqrt{2})$ , is presented as a reproducibility and conceptual-clarity exercise rather than a novelty claim.