"Gauge" in General Relativity: Second-order general relativistic gauge-invariant perturbation theory

As in the case of the other gauge field theories, there is so called gauge'' also in general relativity. This gauge’’ is unphysical degree of freedom. There are two kinds of gauges'' in general relativity. These are called the first- and the second-kind of gauges, respectively. The gauge of the first kind is just coordinate system on a single manifold. On the other hand, the gauge of the second kind arises in the general relativistic perturbations. Through the precise distinction of these two concepts of gauges’', we develop second-order gauge-invariant general relativistic perturbation theory.