E0=1;G=1;c=1;

R=5;T=1/3;

Cte=Sqrt[E/Pi/R^3*E0/(4/T^2+1/R^2)]
Phi=Cte*Exp[-r/2R]*Exp[-t^2/4T^2];
pressure=1/2*( Exp[2F[r,t]]*D[Phi,t]^2+D[Phi,r]^2)

Tsim=10*T;Rsim=10*R;

eqrr=(E^(-2 H[r,t]) (-c^2 E^(2 F[r,t])+E^(2 H[r,t]) (-E^(2 F[r,t]) r^2 (3 (H^(0,1))[r,t]^2+2 (H^(0,2))[r,t])+(c+c r (H^(1,0))[r,t])^2)))/(c^2 r^2)

eqthetatheta=1/c^2 E^(-2 F[r,t]+2 H[r,t]) r (-E^(2 F[r,t]) r ((F^(0,1))[r,t]^2+(F^(0,1))[r,t] (H^(0,1))[r,t]+(H^(0,1))[r,t]^2+(F^(0,2))[r,t]+(H^(0,2))[r,t])+c^2 (-(F^(1,0))[r,t] (1+r (H^(1,0))[r,t])+(H^(1,0))[r,t] (2+r (H^(1,0))[r,t])+r (H^(2,0))[r,t]))



precis=30;
NDSolve[{eqrr==8Pi*G*pressure,eqthetatheta==0,F[r,-Tsim]==0,H[r,-Tsim]==0,(F^(1,0))[0,t]==0 ,(H^(1,0))[0,t]==0,F[Rsim,t]==0,H[Rsim,t]==0 },{F,H},{t,-Tsim,Tsim},{r,0,Rsim},WorkingPrecision->precis,Method->{"MethodOfLines","SpatialDiscretization"->{"TensorProductGrid","MaxPoints"->151,"MinPoints"->151,"DifferenceOrder"->"Pseudospectral"},"TemporalVariable"->t}]