[This][1] paper seems to suggest that the interior metric for a black hole in particular (a.k.a not a different kind of spherically symmetric non-rotating body) is just the exterior Schwarzschild metric but with the $t$ and $r$ coordinates switched. But this doesn’t seem right because the interior metric should really look more like the interior Schwarzschild metric. Am I missing something important here? 

Here is the equation: $ds^2=-(\frac{2M}{t}-1)^{-1}dt^2+(\frac{2M}{t}-1)dr^2+t^2d\Omega^2$


  [1]: https://arxiv.org/pdf/1401.6256