 Trapped circle inside a nonrotating BTZ black hole

For the nonrotating BTZ metric in ingoing coordinates, future null normals to a circle of fixed $v,r$ may be chosen as $\ell ={\partial }_v+(f/2){\partial }_r$ and $n=-{\partial }_r$. Their expansions are ${\theta }_{(\ell )}=f/(2r)$ and ${\theta }_{(n)}=-1/r$, so both are negative inside the outer horizon.