The change in a vector upon parallel transporting it around a closed loop can be expressed in terms of either (1) the area integral of the curvature within the loop or (2) the line integral of the Chr...The change in a vector upon parallel transporting it around a closed loop can be expressed in terms of either (1) the area integral of the curvature within the loop or (2) the line integral of the Christoffel symbol (essentially the gravitational field) on the loop itself.
In this section, which can be skipped at a first reading, we show how the Christoffel symbols can be used to find differential equations that describe geodesics. A geodesic can be defined as a world-l...In this section, which can be skipped at a first reading, we show how the Christoffel symbols can be used to find differential equations that describe geodesics. A geodesic can be defined as a world-line that preserves tangency under parallel transport.
