= Radial timelike incompleteness in Kruskal spacetime
Every maximal radial <timelike geodesic> in positive-mass <Kruskal spacetime> is incomplete in at least one direction. Its equations are $\dot r^2=E^2-1+2M/r$ and $\ddot r=-M/r^2$. A finite turning point is a maximum, and each trajectory reaches $r=0$ at one or both ends. The remaining <proper time> is finite because $d\tau\sim\sqrt{r/(2M)}\,dr$. Complete circular timelike geodesics exist, but they have nonzero <angular momentum>.
Back to article page
