Let us consider the figure eight knot($K$) complement in $S^3$. Let $\gamma$ be an essential simple closed loop inside the figure eight knot complements in $S^3$.Now thicken the knot and consider the tube following the knot. That is the torus following the knot $T$, say. The 1st fundamental group boundary of $S^3 \setminus K$ i.e $\pi_1(S^3 \setminus K)$ is $\mathbb{Z}\oplus\mathbb{Z}$ let us consider the generators $a$ and $b$ let $s$ be the slope on the torus say $s=a^mb^n$ . Let $M$ be a closed 3-manifold manifold attaching a solid torus $D^2 \times S^1$ with respect to the slope $s$.Which is called s-Dehn filling and $M$ is denoted by $M(s)$
1)Does this $\gamma$ simple or not after Dehn filling? If not, are there any conditions on the Dehn filling it will be a simple closed curve in the Dehn-filled manifolds?
Thanks in advance