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Title: Is the string to black hole transition smooth for Schwarzschild black holes?
Plain: If a black hole shrinks until its horizon is as small as a fundamental string, it should turn into a single highly excited string, and the two entropy formulas roughly agree there. Whether this crossover is smooth, with an exact match of states, is not established.
Precise: In weakly coupled string theory in 4D asymptotically flat space, follow a Schwarzschild black hole as the string coupling $g_s$ decreases at fixed entropy until $r_s \sim l_s$. Determine whether the black hole connects continuously to a self-gravitating highly excited string state (Horowitz-Polchinski solution), with the entropy matched including $O(1)$ factors. An answer is a controlled computation of the free energy across $r_s \sim l_s$, or a proof of a phase transition.
Settled by: A computation of the thermodynamics across the correspondence point in $D = 4$ with controlled corrections in $g_s$ and $\ell_s/r_s$.
Kind: well-posed
Answer type: yes-no
References: (empty)
Literature status: partially-resolved
Status note: Chen, Maldacena and Witten (2021) mapped where self-gravitating string solutions exist and how they connect to black holes; exact matching across the transition is open as of 2026.
Posed since: 1993