(* yukterez.net *)

Λ =1/100;H=(Sqrt[Λ /3]);r0=((1/(H^2))^(1/3))+n;v0=0;
gtt=(1-2/r-Λ (r^2)/3);
h=NSolve[gtt==0,r]; h1=h[[3,1,2]]; h2=h[[2,1,2]];
"r Horizont"->{h1,h2}

R[τ_]:=Evaluate[r[τ]/.sol];
v[τ_]:=(((Sqrt[3]) R'[τ] (Sqrt[R[τ]]))/(Sqrt[-6+3 R[τ]+3 ((R'[τ])^2) R[τ]-((R[τ])^3) Λ]));
T[ξ_]:=Quiet[Ξ/.FindRoot[R[Ξ]-ξ,{Ξ,1}]];

n=+0.001;

sol=NDSolve[{
t''[τ]==-((2 (-3+Λ ((r[τ])^3)) r'[τ] t'[τ])/(r[τ] (6-3 r[τ]+Λ ((r[τ])^3)))),
t'[0]==(((Sqrt[3]) (Sqrt[-(r0/(6-3 r0+Λ (r0^3)))]))/(Sqrt[1-(v0^2)])),
t[0]==0,
r''[τ]==(((-3+Λ ((r[τ])^3)) ((r'[τ])^2))/(r[τ](6-3 r[τ]+Λ ((r[τ])^3))))-(((6-3 r[τ]+Λ ((r[τ])^3)) ((-3+Λ ((r[τ])^3)) ((t'[τ])^2)))/(9 ((r[τ])^3))),
r'[0]==(v0/((Sqrt[3]) (Sqrt[1-(v0^2)]) (Sqrt[-(r0/(6-3 r0+(r0^3) Λ))]))),
r[0]==r0},{t,r},{τ,0,500}];

p1=Plot[{v[T[я]]} ,{я,r0,h2},GridLines->{{h1,h2,r0},{0,1}},PlotRange->{{0,h2},{-1,1}},Frame->True,AxesOrigin->{0,0},ImageSize->400,ImagePadding->32];

n=-0.001;

sol=NDSolve[{
t''[τ]==-((2 (-3+Λ ((r[τ])^3)) r'[τ] t'[τ])/(r[τ] (6-3 r[τ]+Λ ((r[τ])^3)))),
t'[0]==(((Sqrt[3]) (Sqrt[-(r0/(6-3 r0+Λ (r0^3)))]))/(Sqrt[1-(v0^2)])),
t[0]==0,
r''[τ]==(((-3+Λ ((r[τ])^3)) ((r'[τ])^2))/(r[τ](6-3 r[τ]+Λ ((r[τ])^3))))-(((6-3 r[τ]+Λ ((r[τ])^3)) ((-3+Λ ((r[τ])^3)) ((t'[τ])^2)))/(9 ((r[τ])^3))),
r'[0]==(v0/((Sqrt[3]) (Sqrt[1-(v0^2)]) (Sqrt[-(r0/(6-3 r0+(r0^3) Λ))]))),
r[0]==r0},{t,r},{τ,0,500}];

p2=Plot[{v[T[я]]} ,{я,h1,r0},GridLines->{{h1,h2,r0},{0,1}},PlotRange->{{0,h2},{-1,1}},Frame->True,AxesOrigin->{0,0},ImageSize->400,ImagePadding->32];

Show[p1,p2]
Quit[]