ClearAll[rmax ,a,l, En,eps]
Needs["PlotLegends`"]
rmax=25;
a = 1;
En=0;
En = ((-1)/3);(*Kerr extremal ISCO*)
(*En = 0;*)
eps=(Sqrt[2 En+1])
VeffSch[r_,l_]:=-(1/r)+((l^2)/(2(r^2)))-((l^2)/(r^3));
VeffKerr[r_,l_]:=-(1/r)+(((l^2)-(a^2)((eps^2)-1))/(2(r^2)))-((((l-a eps))^2)/(r^3));
VeffNewt[r_,l_]:=-(1/r)+((l^2)/(2(r^2)));
VeffSchph[r_,l_]:=((l^2)/(2(r^2)))-((l^2)/(r^3));
VeffKerrph[r_,l_]:=(((l^2)-(a^2)((eps^2)-1))/(2(r^2)))-((((l-a eps))^2)/(r^3));

(*interesting Schwarzschild values*)
(*l=(Sqrt[12]);
l=4;*)
(*interesting Kerr values*)
(*l = 2;*)
(*l=(2/(Sqrt[3]));*)
l=1;
Plot[{VeffNewt[r,l],VeffSch[r,l],VeffKerr[r,l],En},{r,0,rmax},PlotRange->{{0,rmax},{-0.4,0.4}},PlotStyle->{{Red,Dashed,Thick},{Blue,Thick},{Green,Dashing[{.02,.02}],Thick},{Black,Dotted,Thick}},Frame->True,FrameLabel->{"r[M]","(Subscript[V, eff, massive])"},LabelStyle->Directive[Black,FontSize->24], PlotLegend->{Style["Newton",24],Style["Schw",24],Style["Kerr",24],Style["pseudo-Energy",24]},LegendPosition->{.2,.2},LegendSize->{.8,.4},LegendShadow->None,AxesOrigin->{0,0}]
(*Plot[{VeffNewt[r,l],VeffSch[r,l],VeffSchph[r,l],En},{r,0,rmax},PlotRange->{{0,rmax},{-0.4,0.4}},PlotStyle->{{Red,Dashed,Thick},{Blue,Thick},{Green,Dashing[{.02,.02}],Thick},{Black,Dotted,Thick}},Frame->True,FrameLabel->{"r[M]","(Subscript[V, eff])"},LabelStyle->Directive[Black,FontSize->24], PlotLegend->{Style["Newton",24],Style["Schw, massive",24],Style["Schw, photon",24],Style["pseudo-Energy",24]},LegendPosition->{.2,.2},LegendSize->{.8,.4},LegendShadow->None,AxesOrigin->{0,0}]
Plot[{VeffNewt[r,l],VeffKerr[r,l],VeffKerrph[r,l],En},{r,0,rmax},PlotRange->{{0,rmax},{-0.4,0.4}},PlotStyle->{{Red,Dashed,Thick},{Blue,Thick},{Green,Dashing[{.02,.02}],Thick},{Black,Dotted,Thick}},Frame->True,FrameLabel->{"r[M]","(Subscript[V, eff])"},LabelStyle->Directive[Black,FontSize->24], PlotLegend->{Style["Newton",24],Style["Kerr, massive",24],Style["Kerr, photon",24],Style["pseudo-Energy",24]},LegendPosition->{.2,.2},LegendSize->{.8,.4},LegendShadow->None,AxesOrigin->{0,0}]*)