represents the density of mass of the matter, the gravitational equations for electromagnetic fields yield
for
happens to be a quantity which vanishes in all electromagnetic fields. Hence, we realise that in regions of space where electromagnetic fields are present, but all matter is absent, the Gaussian curvature
of space-time always vanishes; whereas in regions occupied by matter it is equal to the density of the matter, and does not vanish.
Before proceeding to compare these various types of curvature, let us recall that there exist three types of tensors of curvature of especial importance: the Riemann-Christoffel tensor
