TikZJax-live

\usepackage{tikz}
\usetikzlibrary{decorations.pathmorphing}

\begin{document}
\begin{tikzpicture}
\node (I)    at ( 4,0)   {I};
\node (II)   at (-4,0)   {II};
\node (III)  at (0, 2.5) {III};
\node (IV)   at (0,-2.5) {IV};

\path  % Four corners of left diamond
  (II) +(90:4)  coordinate[label=90:$i^+$]  (IItop)
       +(-90:4) coordinate[label=-90:$i^-$] (IIbot)
       +(0:4)   coordinate                  (IIright)
       +(180:4) coordinate[label=180:$i^0$] (IIleft)
       ;
\draw (IIleft) -- 
          node[midway, above left]    {$\cal{J}^+$}
          node[midway, below, sloped] {$\bar{u}=\infty$}
      (IItop) --
          node[midway, below, sloped] {$\bar{u}=0$}
      (IIright) -- 
          node[midway, below, sloped] {$\bar{u}=0$}
      (IIbot) --
          node[midway, above, sloped] {$\bar{v}=-\infty$}
          node[midway, below left]    {$\cal{J}^-$}    
      (IIleft) -- cycle;

\path % Four conners of the right diamond (no labels this time)
   (I) +(90:4)  coordinate (Itop)
       +(-90:4) coordinate (Ibot)
       +(180:4) coordinate (Ileft)
       +(0:4)   coordinate (Iright)
       ;
% No text this time in the next diagram
\draw  (Ileft) -- (Itop) -- (Iright) -- (Ibot) -- (Ileft) -- cycle;

% Squiggly lines
\draw[decorate,decoration=zigzag] (IItop) -- (Itop)
      node[midway, above, inner sep=2mm] {$r=0$};

\draw[decorate,decoration=zigzag] (IIbot) -- (Ibot)
      node[midway, below, inner sep=2mm] {$r=0$};

\end{tikzpicture}
\end{document}

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