geodesic_n.hpp File Reference

RK4 geodesic integrator for an (N+1)-dimensional Lorentzian manifold. More...

#include "christoffel_n.hpp"
#include "n_asset_manifold.hpp"
#include <optional>
#include <vector>
#include <Eigen/Dense>

Go to the source code of this file.

Classes
struct	srfm::tensor::GeodesicState
	Position and 4-velocity state on the manifold. More...
class	srfm::tensor::GeodesicSolverN
	RK4 integrator for geodesics on an NAssetManifold. More...

Namespaces
namespace	srfm
namespace	srfm::tensor

Detailed Description

RK4 geodesic integrator for an (N+1)-dimensional Lorentzian manifold.

Module: include/srfm/tensor/ Stage: 4 — N-Asset Manifold

Responsibility

Numerically integrate the geodesic equation

d²x^λ/dτ² = -Γ^λ_μν (dx^μ/dτ)(dx^ν/dτ)

as the first-order system

dx^λ/dτ = u^λ du^λ/dτ = -Σ_{μν} Γ^λ_μν u^μ u^ν

using a classic 4th-order Runge–Kutta scheme.

Guarantees

• Thread-safe: GeodesicSolverN is stateless.
• All public methods are noexcept.
• All fallible operations return std::optional.

NOT Responsible For

• Adaptive step-size control.
• Parallel transport of other tensors along the geodesic.

Definition in file geodesic_n.hpp.