What the paper is about: The author studies a simple observable that follows a particle falling into a three‑dimensional black hole (a BTZ black hole). One operator of a two‑point correlation function stays outside the hole. The other follows the infaller on a timelike path. The calculation shows the correlator blows up — it diverges — when the infaller reaches the black hole singularity.

What the researchers did and how they studied it: The bulk calculation uses a standard trick called the method of images to write the BTZ propagator as a sum of Anti‑de Sitter (AdS) propagators. The same bulk object can be rewritten as an integral over a boundary correlation function using the HKLL (Hamilton–Kabat–Lifschytz–Lowe) kernel. At large central charge (a parameter that controls how classical the boundary theory is), the boundary correlator separates into a vacuum part and exchanges of so‑called double‑twist operators. The paper finds that the divergence at the singularity comes entirely from the double‑twist sector. A second kind of singularity also appears when the exterior point lines up with an image of the infaller; an infinite sequence of these image singularities clusters near the singularity.

What new physics changes the picture: The author then adds a tower of massive particles whose number grows exponentially with mass (this is described as Hagedorn growth). Such a tower produces loop corrections to the propagator. As the infaller approaches the singularity, the length of loops attached to the infalling path shrinks to zero. With many states available, the sum of loop effects diverges in the same way known as a Hagedorn transition in thermal physics. In other words, loop corrections become large near the singularity and swamp the simple, tree‑level result. The paper works with an effective field theory of the tower and does not assume a specific string theory completion.