Einstein’s Theory of Gravity

Abstract

Special Relativity can be described as physics in a 4-dimensional space-time manifold $\mathcal {M}$ with metric tensor g _μν that reduces to η _μν = diag(−1, +1, +1, +1) in any global inertial coordinate system. Such selected global coordinates exist because the geometry of Minkowskian space-time is flat, i.e., the curvature and Ricci tensor vanish. Einstein’s theory of gravity is also a structure $(\mathcal {M},g)$, but space-time geometry in the presence of gravitational fields is not longer flat, the curvature tensor describing the tidal actions. For vanishing gravitational fields the structure $(\mathcal {M},g)$ reduces to the Minkowskian space-time; it is fully in accordance with all experiments from Special Relativity.