This observation combined with general covariance has profound implications for GR.

Einstein emphasized the importance of general covariance for the development of general relativity.

Due to its general covariance, Einstein's theory is not sufficient by itself to determine the time evolution of the metric tensor.

Writing an equation in manifestly covariant form is useful because it guarantees general covariance upon quick inspection.

In short, in general relativity, time is just another coordinate as a result of general covariance.

Other hidden symmetries of physics include gauge symmetry and general covariance.

The symmetry is called general covariance or diffeomorphism invariance.

The principle of general covariance works on the assumption that spacetime is smooth and continuous.

When Einstein realized that general covariance was actually tenable, he quickly completed the development of the field equations that are named after him.

In 1913, Einstein (erroneously) concluded from his hole argument that general covariance was not viable.