In this article discussing this and related papers, it is explained among other things, how the neighborhood of an observer's worldline can be approximated by a region of Minkowsky spacetime.

If I understand this right (corrections of confused fluff and misunderstandings are highly welcome), a coordinate transformation which depends on the observer's current location $p_0$ in the classical backround spacetime, to a free falling local Lorentz frame is applied. In this reference frame, local coordinates ($\tau$, $\theta$, $\phi$) together with a parameter $\lambda$ (which describes the location on the observer's worldline?) can be used. As $\lambda$ deviates too mach from $\lambda(p_0)$, the local proper acceleration $\sqrt{a_{\mu}a^{\mu}}$ becames large and approaches the string scale (is this because flat Minkowsky space is only locally valid?) and stringy effects kick in.

The authors postulate that at these points (called the gravitational observer horizon) some microscopic degrees of freedom have to exist that give rise to the Beckenstein-Hawking entropy describing the entropy contained in spacetime beyond the gravitational observer horizon (?).

This is quite a long text to introduce my question, which simply is: Can these microstates be described by the fuzzball conjecture or what are they assumed to "look" like?