geodesic_solver.hpp File Reference

RK4 geodesic integrator on a spacetime manifold (AGT-13 / SRFM) More...

#include <array>
#include <cmath>
#include <optional>
#include "../manifold/spacetime_manifold.hpp"

Go to the source code of this file.

Classes
struct	srfm::geodesic::GeodesicState
	State of a particle on a geodesic: position x^μ and 4-velocity u^μ. More...
class	srfm::geodesic::GeodesicSolver

Namespaces
namespace	srfm
namespace	srfm::geodesic

Detailed Description

RK4 geodesic integrator on a spacetime manifold (AGT-13 / SRFM)

Module: src/geodesic/ Owner: AGT-13 (Adversarial hardening) — 2026-03-01

Responsibility

Numerically integrate the geodesic equation:

d²x^λ/dτ² + Γ^λ_μν (dx^μ/dτ)(dx^ν/dτ) = 0

using a 4th-order Runge-Kutta scheme.

Key property (tested by property suite): On the flat Minkowski metric (all Γ = 0) the solution is a straight line. Geodesic deviation after 100 RK4 steps is < 1e-8 from the linear prediction.

Design Constraints

• Must always terminate (no unbounded loops; step count is bounded). • RK4 must not produce NaN even for extreme initial conditions. • All fallible operations return std::optional. • noexcept throughout.

NOT Responsible For • Adaptive step-size control. • Parallelisation across multiple geodesics. • Non-metric coupling terms (e.g. electromagnetic).

Definition in file geodesic_solver.hpp.