Crate autograv 

autograv

Numerical-relativity tensor calculus built on top of diffable’s typed tensor algebra and forward-mode automatic differentiation.

The crate evaluates a user-supplied MetricField and computes:

• Christoffel symbols and torsion;
• Riemann curvature;
• Ricci tensor and scalar;
• Kretschmann invariant;
• Einstein tensor and stress-energy-momentum tensor.

Metric functions are generic over their scalar type, allowing diffable’s Taylor jets to flow through the metric and connection formulas. The public jacobian_of bridge in ad performs the seed/extract operation required for tensor-valued maps, which diffable 0.5.0 does not yet represent through its d(f) blanket implementation.

Quick start

use autograv::{as_t3, christoffel_symbols, ricci_scalar, SphericalPolar};
use diffable::coords::Coords;

let metric = SphericalPolar;
let point = Coords([5.0, std::f64::consts::FRAC_PI_3, std::f64::consts::FRAC_PI_2]);
let gamma = as_t3::<3>(&christoffel_symbols(&metric, &point));

assert!((gamma[0][1][1] + 5.0).abs() < 1e-12); // Γ^r_θθ = −r
assert_eq!(ricci_scalar(&metric, &point), 0.0); // flat R³ in spherical coordinates

Coordinate conventions

Coords<f64, N> is used as the coordinate presentation. The metric values, not the Coords type parameter, define the physical signature; for example, Minkowski supplies (-,+,+,+) and Schwarzschild supplies its Lorentzian diagonal components.

Numerical convention

Public tensor results are rounded componentwise to zero when their absolute value is below TOLERANCE, matching the Python implementation’s close_to_zero decorator. A singular metric panics during inversion; callers must evaluate only at nonsingular coordinate points. TODO: a better API surface than panicking?

Re-exports

pub use gr::Christoffel;

pub use gr::Ricci;

pub use gr::Riemann;

pub use gr::christoffel_symbols;

pub use gr::einstein_tensor;

pub use gr::kretschmann_invariant;

pub use gr::ricci_scalar;

pub use gr::ricci_tensor;

pub use gr::riemann_tensor;

pub use gr::stress_energy_momentum_tensor;

pub use gr::torsion_tensor;

pub use metric::MetricField;

pub use metric::MetricTensor;

pub use metric::Minkowski;

pub use metric::ScalarConst;

pub use metric::Schwarzschild;

pub use metric::SphericalPolar;

pub use tensor::T1;

pub use tensor::T2;

pub use tensor::T3;

pub use tensor::T4;

pub use tensor::TOLERANCE;

pub use tensor::as_t2;

pub use tensor::as_t3;

pub use tensor::as_t4;

pub use tensor::close_to_zero;

pub use tensor::close_to_zero_scalar;

Modules

ad

Forward-mode Jacobians over diffable’s truncated Taylor jets.

gr

General-relativity index algebra: connection, curvature, and Einstein field equations.

metric

Metric fields. A metric is a function from coordinates to a covariant (0, 2) tensor field, generic over the scalar so diffable’s jets flow through every layer of differentiation.

tensor

Flat index algebra over tensor coordinates.