Metric Tensor

The space-time metric (pseudo-Euclidean) is defined by the tensor

$$g_{\mu\nu} = \left( \begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 ... ... & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{array}\right)$$ (2.9)

or $g_{00}=1$, $g_{kk}=-1$, and $g_{\mu\nu}=0$ if $\mu\neq\nu$.