= Solution
Universality of <free fall> equates the passive gravitational response to <inertial mass> up to a universal choice of units. The <Einstein equivalence principle> further states that local nongravitational experiments in a freely falling laboratory obey <special relativity> independently of the laboratory's location and <velocity>. A supported laboratory instead has <proper acceleration>, just as an accelerating laboratory in flat spacetime does.
Around an event, freely falling coordinates can be chosen so that $g_{\mu\nu}=\eta_{\mu\nu}$ and $\Gamma^\alpha{}_{\mu\nu}=0$ there. The first <metric tensor> <derivatives> vanish at that event, and nearby corrections begin at order curvature times squared separation. The <metric tensor>'s second <derivatives> retain the <Riemann tensor>. Thus \b[a <local inertial frame> removes <Christoffel symbols> at an event, while tidal gravity remains measurable over a finite region]. Relative motion of separated freely falling test particles detects this curvature through <geodesic deviation>. Freely falling axes carried along an observer's <world line> extend the local construction, but do not make an extended curved region globally Minkowskian.
Back to article page
