srfm::tensor::GeodesicSolver Class Reference

#include <tensor.hpp>

Public Member Functions
	GeodesicSolver (const MetricTensor &metric, double step_size=constants::DEFAULT_GEODESIC_STEP, double christoffel_h=constants::DEFAULT_FD_STEP)
std::vector< GeodesicState >	integrate (const SpacetimePoint &x0, const FourVelocity &u0, int steps) const
double	norm_squared (const SpacetimePoint &x, const FourVelocity &u) const

Detailed Description

Integrates the geodesic equation using classical 4th-order Runge-Kutta.

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

describes the "free fall" path of an asset price in curved financial spacetime — the trajectory that minimises proper time (the path of least market resistance given the covariance geometry).

Example

auto g   = MetricTensor::make_minkowski(1.0, 0.2);
auto sol = GeodesicSolver(g, 0.01);
srfm::SpacetimePoint x0 = srfm::SpacetimePoint::Zero();
srfm::FourVelocity   u0; u0 << 1.0, 0.1, 0.0, 0.0;
auto traj = sol.integrate(x0, u0, 100);

Definition at line 553 of file tensor.hpp.

Constructor & Destructor Documentation

GeodesicSolver()

srfm::tensor::GeodesicSolver::GeodesicSolver	(	const MetricTensor &	metric,
		double	step_size = constants::DEFAULT_GEODESIC_STEP,
		double	christoffel_h = constants::DEFAULT_FD_STEP
	)

Construct with a metric, proper-time step size, and FD step for Γ.

Arguments

• metric — Position-dependent metric tensor
• step_size — Proper-time step dτ for RK4 integration
• christoffel_h — Finite-difference step for Christoffel symbols

Definition at line 18 of file geodesic.cpp.

Member Function Documentation

integrate()

std::vector< GeodesicState > srfm::tensor::GeodesicSolver::integrate	(	const SpacetimePoint &	x0,
		const FourVelocity &	u0,
		int	steps
	)		const

Integrate the geodesic from (x0, u0) for steps proper-time steps.

Arguments

• x0 — Initial spacetime position
• u0 — Initial four-velocity (tangent vector)
• steps — Number of RK4 integration steps

Returns

Vector of steps + 1 states including the initial state.

Definition at line 54 of file geodesic.cpp.

norm_squared()

double srfm::tensor::GeodesicSolver::norm_squared	(	const SpacetimePoint &	x,
		const FourVelocity &	u
	)		const

Compute g_μν u^μ u^ν to diagnose the causal character of the geodesic.

Returns

• Negative: timelike (subluminal price movement — physically meaningful)
• Zero: null / lightlike (speed-of-information signal)
• Positive: spacelike (acausal — indicates model error or extreme regime)

Definition at line 75 of file geodesic.cpp.

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The documentation for this class was generated from the following files:

• include/srfm/tensor.hpp
• src/tensor/geodesic.cpp