Figure 1

Schematic picture of two particles falling into a black hole with angular momentum $a$ (per unit black hole mass) and colliding near the horizon. The allowed range of $l$ for geodesics falling into the black hole is also given.Reuse & Permissions

Figure 2

For a Schwarzschild black hole (a) shows the variation of $\dot{r}$ with radius for three different values of angular momentum $l=2$, 4, and 5. For $l=5$, $\dot{r}$ reaches zero, indicating a turning point, before reaching the horizon. These geodesics are not interesting for us. $l=4$ is a critical case where geodesics start falling in. For smaller values of $|l|$ all geodesics fall in. Panel (b) shows the variation of $E_{\mathrm{c}.\mathrm{m}.}$ with radius for three combinations of $l_1$ and $l_2$. Note the kink corresponding to the critical geodesic with $l=4$. The vertical line at $r=2$ is the horizon, and we see that $E_{\mathrm{c}.\mathrm{m}.}$ is finite in all cases.Reuse & Permissions

Figure 3

For a Kerr black hole with $a=1$ (a) shows the variation of $\dot{r}$ with radius for three different values of angular momentum $l=0.4$, 2, and 3. Panel (b) shows the variation of $E_{\mathrm{c}.\mathrm{m}.}$ with radius for three combinations of $l_1$ and $l_2$. For $l_1=2$ we see that $E_{\mathrm{c}.\mathrm{m}.}$ blows up at the horizon.Reuse & Permissions