srfm::tensor::MetricTensor Class Reference

#include <tensor.hpp>

Public Member Functions
	MetricTensor (MetricFunction metric_fn)
	Construct from an arbitrary position-dependent metric function.
MetricMatrix	evaluate (const SpacetimePoint &x) const
void	evaluate_into (const SpacetimePoint &x, MetricMatrix &out) const
std::optional< MetricMatrix >	inverse (const SpacetimePoint &x) const
bool	is_lorentzian (const SpacetimePoint &x) const
double	spacetime_interval (const SpacetimePoint &x, const FourVelocity &dx) const

Static Public Member Functions
static MetricTensor	make_minkowski (double time_scale=1.0, double spatial_scale=1.0)
static MetricTensor	make_diagonal (double time_scale, const std::array< double, 3 > &vol)
static MetricTensor	make_from_covariance (double time_scale, const Eigen::Matrix3d &cov)

Detailed Description

A position-dependent 4×4 symmetric tensor g_μν encoding the geometry of the financial spacetime manifold.

The metric signature is (−,+,+,+): component 0 is timelike (market time), components 1–3 are spacelike (asset returns). Off-diagonal spatial entries encode asset correlations; off-diagonal time-space entries encode temporal momentum correlations.

Example

// Flat market: uncorrelated assets, equal volatility 0.2
auto g = srfm::tensor::MetricTensor::make_minkowski(1.0, 0.2);
srfm::SpacetimePoint origin = srfm::SpacetimePoint::Zero();
auto gx = g.evaluate(origin);  // diag(-1, 0.04, 0.04, 0.04)

Definition at line 167 of file tensor.hpp.

Constructor & Destructor Documentation

MetricTensor()

srfm::tensor::MetricTensor::MetricTensor ( MetricFunction  metric_fn )

explicit

Construct from an arbitrary position-dependent metric function.

Definition at line 23 of file metric_tensor.cpp.

Member Function Documentation

evaluate()

MetricMatrix srfm::tensor::MetricTensor::evaluate

(

const SpacetimePoint &

x

)

const

Evaluate g_μν at the given spacetime point.

Arguments

• x — Position in the 4D financial spacetime manifold

Returns

The 4×4 metric matrix at x.

Definition at line 28 of file metric_tensor.cpp.

evaluate_into()

void srfm::tensor::MetricTensor::evaluate_into ( const SpacetimePoint &  x, MetricMatrix &  out  ) const

inline

Evaluate g_μν at x and store the result into out (in-place overload).

Avoids an extra copy compared to evaluate() when the caller already holds a MetricMatrix to overwrite.

Arguments

• x — Position in the 4D financial spacetime manifold
• out — Output matrix to overwrite with g_μν(x)

Definition at line 189 of file tensor.hpp.

inverse()

std::optional< MetricMatrix > srfm::tensor::MetricTensor::inverse

(

const SpacetimePoint &

x

)

const

Compute the inverse metric g^μν at point x.

Returns

• Some(g_inv) if the metric is invertible at x
• None if the metric is singular (degenerate correlations)

Definition at line 32 of file metric_tensor.cpp.

is_lorentzian()

bool srfm::tensor::MetricTensor::is_lorentzian

(

const SpacetimePoint &

x

)

const

Return true if the metric has Lorentzian signature (−,+,+,+) at x. A Lorentzian metric has exactly one negative eigenvalue.

Definition at line 75 of file metric_tensor.cpp.

make_diagonal()

MetricTensor srfm::tensor::MetricTensor::make_diagonal ( double  time_scale, const std::array< double, 3 > &  vol  )

static

Diagonal metric from per-asset volatilities: g = diag(−time_scale², σ₁², σ₂², σ₃²).

Arguments

• time_scale — Scale of the time dimension
• vol — Array of three asset volatilities {σ₁, σ₂, σ₃}

Definition at line 120 of file metric_tensor.cpp.

make_from_covariance()

MetricTensor srfm::tensor::MetricTensor::make_from_covariance ( double  time_scale, const Eigen::Matrix3d &  cov  )

static

Full covariance-based metric from a 3×3 asset covariance matrix. g = block-diag(−time_scale², Σ) where Σ is the asset covariance.

Arguments

• time_scale — Scale of the time dimension
• cov — 3×3 asset covariance matrix (must be positive definite)

Definition at line 132 of file metric_tensor.cpp.

make_minkowski()

MetricTensor srfm::tensor::MetricTensor::make_minkowski ( double  time_scale = 1.0, double  spatial_scale = 1.0  )

static

Flat Minkowski-like metric: g = diag(−time_scale², σ², σ², σ²).

Equivalent to a market with uncorrelated assets of equal volatility σ.

Arguments

• time_scale — Scale of the time dimension (c analogue), default 1
• spatial_scale — Common asset volatility σ, default 1

Definition at line 108 of file metric_tensor.cpp.

spacetime_interval()

double srfm::tensor::MetricTensor::spacetime_interval	(	const SpacetimePoint &	x,
		const FourVelocity &	dx
	)		const

Compute the spacetime interval ds² = g_μν dx^μ dx^ν.

Returns

• Negative: timelike displacement (subluminal market movement)
• Zero: null / lightlike (signal at speed of information)
• Positive: spacelike displacement (acausal — outside light cone)

Definition at line 99 of file metric_tensor.cpp.

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

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