Light cones
In[174]:=
gc2=ParametricPlot3D[{x[t,.6, theta0],y[t,.6, theta0],t},
{t,-5,5},{theta0,-Pi/1.21,Pi/1.21}, AxesLabel -> {"x","y","t"}]

Out[175]=
-Graphics3D-
In[176]:=
gc1=ParametricPlot3D[{x[-t,.6, theta0],y[-t,.6, theta0],t},
{t,-5,5},{theta0,-Pi/1.21,Pi/1.21}, AxesLabel -> {"x","y","t"}]

Out[177]=
-Graphics3D-
In[178]:=
Show[gc1,gc2]

Out[179]=
-Graphics3D-
Up to Plot the results
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