Validity of the Central Dogma for black-hole microstates

Determine whether the Central Dogma holds—that a black hole, as seen by an exterior observer, behaves as a finite quantum system with internal Hilbert-space dimension exp(S_BH), so that the Bekenstein–Hawking entropy S_BH counts all of its microstates.

Background

The notes introduce a quantum-information perspective on black holes via the Page curve and state the Central Dogma: from the viewpoint of an external observer, the black hole has approximately e^{S_BH} internal states, implying that S_BH counts all microstates. This assumption underpins expectations about the rise and fall of radiation entropy during evaporation.

The author explicitly notes that this assumption is disputed, highlighting an active debate about whether black holes can be treated as finite quantum systems of size e^{S_BH} and whether S_BH genuinely counts all microstates relevant to exterior observers.