\documentclass[a4paper]{article}
\begin{document}
\begin{eqnarray*}
\mbox{(1)} \qquad \mbox{d}s^{2}
 & = & \left ( 1 - \frac{2 G M}{r c^{2}} \right ) c^{2} \, \mbox{d}t^{2}
 - \frac{1}{1 - \frac{2 G M}{r c^{2}}} \, \mbox{d}r^{2}
 - r^{2} \sin^{2} \theta \, \mbox{d}\varphi^{2}
 - r^{2} \, \mbox{d}\theta^{2} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\mbox{(2)} \qquad \mbox{d}s^{2}
 & = & \left ( 1 - \frac{2 G M}{r c^{2}} \right ) c^{2} \, \mbox{d}t^{2}
 - \frac{1}{1 - \frac{2 G M}{r c^{2}}} \, \mbox{d}r^{2}
 - r^{2} \sin^{2} \theta \, \mbox{d}\varphi^{2}
 - r^{2} \, \mbox{d}\theta^{2} \\
& = & \left ( 1 - \frac{2 G M}{r c^{2}} \right ) c^{2} \, \mbox{d}t^{2} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\mbox{(3)} \qquad \mbox{d}s^{2}
 & = & c^{2} \, \mbox{d}\tau^{2} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\mbox{(4)} \qquad \left ( 1 - \frac{2 G M}{r c^{2}} \right ) c^{2} \, \mbox{d}t^{2}
 & = & c^{2} \, \mbox{d}\tau^{2} \\
\left ( 1 - \frac{2 G M}{r c^{2}} \right ) \, \mbox{d}t^{2}
 & = & \, \mbox{d}\tau^{2} \\
\frac{\mbox{d}t^{2}}{\mbox{d} \tau^{2}}
 & = & \frac{1}{1 - \frac{2 G M}{r c^{2}}} \\
\frac{\mbox{d}t}{\mbox{d}\tau}
 & = & \frac{1}{\sqrt{1 - \frac{2 G M}{r c^{2}}}} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\mbox{(5)} \qquad E
 & = & h f \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\mbox{(6)} \qquad f
 & = & \frac{1}{T} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\mbox{(7)} \qquad E
 & = & h f \\
& = & \frac{h}{T} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\mbox{(8a)} \qquad E_{1}
 & = & \frac{h}{T_{1}} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\mbox{(8b)} \qquad E_{2}
 & = & \frac{h}{T_{2}} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\mbox{(9)} \qquad \frac{E_{1}}{E_{2}}
 & = & \frac{\frac{h}{T_{1}}}{\frac{h}{T_{2}}} \\
\frac{E_{2}}{E_{1}}
 & = & \frac{T_{1}}{T_{2}} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\mbox{(10)} \qquad \frac{E_{2}}{E_{1}}
 & = & \frac{T_{1}}{T_{2}} \\
& = & \frac{1}{\sqrt{1 - \frac{2 G M}{r c^{2}}}} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\mbox{(11)} \qquad R_{s}
 & = & \frac{2 G M}{c^{2}} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\mbox{(12)} \qquad \frac{E_{2}}{E_{1}}
 & = & \frac{1}{\sqrt{1 - \frac{2 G M}{r c^{2}}}} \\
& = & \frac{1}{\sqrt{1 - \frac{R_{s}}{r}}} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\mbox{(13)} \qquad \lim_{r \to \infty} \frac{E_{2}}{E_{1}}
 & = & \lim_{r \to \infty} \frac{1}{\sqrt{1 - \frac{R_{s}}{r}}} \\
& \approx & \frac{1}{\sqrt{1 - 0}} \\
& = & 1 \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\mbox{(14)} \qquad \lim_{r \to R_{s}} \frac{E_{2}}{E_{1}}
 & = & \lim_{r \to R_{s}} \frac{1}{\sqrt{1 - \frac{R_{s}}{r}}} \\
& \approx & \frac{1}{\sqrt{1 - \frac{R_{s}}{R_{s}}}} \\
& = & \frac{1}{\sqrt{1 - 1}} \\
& = & \infty \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\mbox{(15)} \qquad \frac{E_{1}}{E_{2}}
 & = & \frac{1}{\sqrt{1 - \frac{R_{s}}{r}}} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\mbox{(16)} \qquad z
 & = & \frac{1}{\sqrt{1 - \frac{R_{s}}{r}}} - 1 \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\mbox{(17)} \qquad 1 + z
 & = & \frac{1}{\sqrt{1 - \frac{R_{s}}{r}}} \\
\end{eqnarray*}
\end{document}
