Principal directions in a gravitational field

Extract

In a general metric space of four dimensions, with an interval given by , where – ds² = g_μνdx^μdx^ν, where g = ║g_μν║<0, we can choose locally galilean coordinates at any point. The initial directions of the axes can be fixed in an absolute fashion as the directions of the principal axes of the quadric G_μνdx^μdx^ν = const., is the contracted Riemann-Christoffel tensor.