Solution
= Solution
In <normal coordinates>, each radial line $u(t)=tv$ is an affinely parametrized <geodesic>. Its coordinate <geodesic equation> gives $\Gamma^k_{ij}(tv)v^iv^j=0$. At $t=0$ this holds for every <tangent vector> $v$. Since $\Gamma^k_{ij}=\Gamma^k_{ji}$, polarization of this <quadratic form> gives every coefficient zero. Thus \b[all <Christoffel symbols> vanish at the centre $p$]; they need not vanish elsewhere.