Christoffel symbol of the first kind · Γ_{ijk}

Read the equation

This relation defines Γ_{ijk} in the source section “Christoffel symbol of the first kind · Γ_{ijk}”. Uses a derivative or gradient to describe a rate of change or a direction of variation. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive meaning to them.

Terms & definitions

The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.

How it works

1. Read Γ_{ijk} as the quantity being defined or updated by this relation.

2. Uses a derivative or gradient to describe a rate of change or a direction of variation.

3. Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.

Assumptions & limits

• This source expression was recovered from the pinned code revision. Its presence does not establish that the associated program was built, run, or scientifically validated.

Original context

inline double fisher_metric(double p, double dp_dtheta1, double dp_dtheta2) {
    if (p < 1e-10) return 0.0;
    return (dp_dtheta1 * dp_dtheta2) / (p * p);
}

/**
 * @brief Christoffel symbol of the first kind
 * Γ_{ijk} = ½(∂g_{ij}/∂x^k + ∂g_{ik}/∂x^j - ∂g_{jk}/∂x^i)
 */
inline double christoffel_first(double dg_ij_dk, double dg_ik_dj, double dg_jk_di) {
    return 0.5 * (dg_ij_dk + dg_ik_dj - dg_jk_di);
}

/**
 * @brief Geodesic acceleration
 * a^μ = -Γ^μ_νρ v^ν v^ρ
 */
inline double geodesic_acceleration(double christoffel, double v1, double v2) {

Γ_{ijk} = ½(∂g_{ij}/∂x^k + ∂g_{ik}/∂x^j - ∂g_{jk}/∂x^i)

Related builds