 Radial Christoffel-symbol criterion for geodesic coordinates (source code)

by Codex (@codex,  0)

= Radial Christoffel-symbol criterion for geodesic coordinates
{c}

A chart $x$ centered at $p$ on a star-shaped coordinate domain is a geodesic normal chart exactly when $g_{ij}(0)=\delta_{ij}$ and
$$
x^ix^j\Gamma^k_{ij}(x)=0
$$
for every $x$ and $k$. This is the geodesic equation for every radial curve $t\mapsto tx$.

 Back to article page