Gravitation and Cosmology

In his special theory of relativity, Einstein introduced the notion of equivalence between different inertial frames of reference. These are reference frames which have a uniform motion with respect to each other and are free from inertial forces. According to the principle of covariance, the laws of physics have the same mathematical form if properly expressed in arbitrary inertial frames of reference. Tensor analysis is a convenient tool for the formulation of the Einstein's principle of covariance. It will be described in the next section that tensors transform in a special way between different coordinate systems, allowing a uniform and elegant way of writing the fundamental laws of nature.