Tortoise coordinate of a five-dimensional charged black hole
= Tortoise coordinate of a five-dimensional charged black hole
{title2=$\frac{dr_\star}{dr}=\frac1f$}
For distinct horizon radii $a>b>0$, integrating $dr_\star/dr=f^{-1}$ gives $r_\star=r+\frac{a^3}{2(a^2-b^2)}\log|(r-a)/(r+a)|-\frac{b^3}{2(a^2-b^2)}\log|(r-b)/(r+b)|+C$. The <tortoise coordinate> defines constant retarded or advanced coordinates on radial <null geodesics>.