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-

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Plot the results