 The Christoffel symbols find frequent use in Einstein's theory of general relativity, where spacetime is represented by a curved 4-dimensional Lorentz manifold with a Levi-Civita connection.The Einstein field equations – which determine the geometry of spacetime in the presence of matter – contain the Ricci tensor.Since the Ricci tensor is derived from the Riemann curvature tensor, which can be written in terms of Christoffel symbols, a calculation of the Christoffel symbols is essential.