Featured research software · Wolfram Language

RAY.

Relativity and Geometry Toolkit

Explicit-component tensor geometry, curvature invariants, and Raychaudhuri kinematics for Mathematica and Wolfram Language.

Version 1.0.0MIT licenseActive development

View on GitHub ↗Documentation ↗

Text-free black hole illustration with curved spacetime grid

Available in v1.0.0

Current working features

These capabilities are documented in the current public release. RAY works with explicit metric components rather than requiring an abstract-index workflow.

01 / IMPLEMENTED

Tensor geometry

Arbitrary-dimensional explicit metrics and metric signatures
Christoffel symbols and Riemann, Ricci, Einstein, and Weyl tensors
Ricci scalar, Kretschmann invariant, and quadratic Ricci/Weyl invariants
Configurable raised, lowered, and mixed tensor indices

02 / IMPLEMENTED

Congruence & Raychaudhuri

Normalized non-null congruences and covariant derivatives
Expansion, acceleration, shear, and vorticity
Shear and vorticity scalars; Ricci contraction along the congruence
Raychaudhuri terms, equation residual, and kinematical consistency checks

03 / IMPLEMENTED

Research workflow

Nonzero component tables and notebook-friendly formatted output
Access to raw symbolic expressions for further calculations
One-command geometry, kinematics, and full reports
Example calculations and regression tests

Getting started

A straightforward Mathematica workflow.

Install RAY as a Wolfram application or paclet, then load the package, define a metric, and inspect its geometric quantities. See the repository for full installation options.

Installation guide ↗

WOLFRAM LANGUAGEQuick start

Needs["RAY`"]
RAYHelp[]

(* After defining a metric *)
RAYRicciScalar[]
RAYKretschmann[]
RAYRaychaudhuriTerms[]

See complete examples ↗

Development roadmap

Future implementation

Planned or exploratory — not available in v1.0.0. The roadmap describes intended research directions, not guaranteed features or release dates.

ROADMAP / 01

Near term

More regression tests, validation, and example spacetimes
Improved tensor symmetry handling, sparse calculations, and performance
Expanded documentation and benchmark coverage

ROADMAP / 02

Geometry & interoperability

Coordinate transformations, geodesics and geodesic deviation
Tetrads/vielbeins, differential forms, spin connections, and ADM 3+1
xAct import/export and abstract-index interoperability

ROADMAP / 03

Higher-dimensional gravity

p-forms, Hodge duality, flux stress tensors, and Bianchi identities
Warped products, dimensional reduction and compactification tools
Gamma matrices, Killing spinors and supergravity equations of motion

Full development roadmap ↗Regression tests ↗

Author & maintainer

Shaikot Jahan Shuvo · Original author, mathematical direction, and maintenance. Featured by the SAM Research Group; repository ownership remains with its creator.

Repository & contributions ↗