Schwarschild libname:="/Users/mark/math/Msh/Exterior/beta",libname:with(Exterior):exterior([t,r,theta,phi]);Next we create the contact forms and the exterior differential system for this equationM:=sqrt(1-2*m/r);Moving FrameTheta:=<M*dt,dr/M,r*dtheta,r*sin(theta)*dphi>;eta:=DiagonalMatrix([1,-1,-1,-1]);simplify(MetricConnection(Theta,eta));simplify(Curvature(%),symbolic);Coordinate FrameCoord_Frame:=<dt,dr,dtheta,dphi>;g:=DiagonalMatrix([M^2,-1/M^2,-r^2,-r^2*sin(theta)^2]);MetricConnection(Coord_Frame,g);Coord_Curv:=Curvature(%);Null TetradNull_Tetrad:=<M^2/2*dt-dr/2,dt+1/M^2*dr,1/sqrt(2)*(dtheta+I*sin(theta)*dphi),1/sqrt(2)*(dtheta-I*sin(theta)*dphi)>;null_metric:=<<0,1,0,0>|<1,0,0,0>|<0,0,0,-1>|<0,0,-1,0>>;Null_Connection:=MetricConnection(Null_Tetrad,null_metric);d(Null_Tetrad)+Null_Connection^Null_Tetrad;simplify(%);Null_Curv:=Curvature(Null_Connection);d(Null_Connection)+Null_Connection^Null_Connection;