Inverse of

doug  <sweetser@world.std.com>

qCurved[t_, x_, y_, z_] :=  (({{t Exp[-((G M)/((C^2)(Sqrt[(x^2)+(y^2)+(z^2)])))], -x Exp[((G M)/((C^2)(Sqrt[(x^2)+(y^2)+(z^2)])))], -y Exp[((G M)/((C^2)(Sqrt[(x^2)+(y^2)+(z^2)])))], -z Exp[((G M)/((C^2)(Sqrt[(x^2)+(y^2)+(z^2)])))]}, {x Exp[((G M)/((C^2)(Sqrt[(x^2)+(y^2)+(z^2)])))], t Exp[-((G M)/((C^2)(Sqrt[(x^2)+(y^2)+(z^2)])))], -z Exp[((G M)/((C^2)(Sqrt[(x^2)+(y^2)+(z^2)])))], y Exp[((G M)/((C^2)(Sqrt[(x^2)+(y^2)+(z^2)])))]}, {y Exp[((G M)/((C^2)(Sqrt[(x^2)+(y^2)+(z^2)])))], z Exp[((G M)/((C^2)(Sqrt[(x^2)+(y^2)+(z^2)])))], t Exp[-((G M)/((C^2)(Sqrt[(x^2)+(y^2)+(z^2)])))], -x Exp[((G M)/((C^2)(Sqrt[(x^2)+(y^2)+(z^2)])))]}, {z Exp[((G M)/((C^2)(Sqrt[(x^2)+(y^2)+(z^2)])))], -y Exp[((G M)/((C^2)(Sqrt[(x^2)+(y^2)+(z^2)])))], x Exp[((G M)/((C^2)(Sqrt[(x^2)+(y^2)+(z^2)])))], t Exp[-((G M)/((C^2)(Sqrt[(x^2)+(y^2)+(z^2)])))]}}))

Simplify[Inverse[qCurved[t,x,y,z]/.G->0].{1,0,0,0}]

Simplify[Inverse[qCurved[t,x,y,z]].{1,0,0,0}]