Microscopic origin of the Bekenstein–Hawking entropy

Identify the microscopic degrees of freedom counted by the Bekenstein–Hawking entropy S_BH of a black hole and establish a concrete microphysical interpretation of S_BH as the logarithm of the number of black-hole microstates compatible with the macroscopic parameters (mass M and angular momentum L).

Background

In the semi-classical framework, black holes possess a thermodynamic entropy—the Bekenstein–Hawking entropy—proportional to the horizon area. The notes connect this macroscopic quantity to Hawking radiation and discuss mass and spin loss via quantum emission, but emphasize that the microscopic nature of the degrees of freedom responsible for S_BH is unresolved.

Clarifying the microphysical content of S_BH would ground the thermodynamic description of black holes in an underlying statistical picture and determine precisely what the entropy counts—i.e., which degrees of freedom encode the enormous state count implied by the area law.

References

It remains an open question what microscopic degrees of freedom S_{\rm BH} counts, but the standard interpretation is that it measures the logarithm of the number of microstates compatible with the macroscopic parameters (M,L).

— Benasque Lectures on Gaussian Bosonic Systems and Analogue Gravity  (2512.24344 - Brady, 30 Dec 2025) in Part IV, Section "Semi-classical evolution"

Discriminating between them requires input the first law cannot supply --- a microcanonical count of remnant states, or a Euclidean evaluation of the partition function of the extremal throat. We regard this as the sharpest open question raised by the present analysis.

— Entanglement islands and information recovery from near-extremal regular black holes  (2608.18603 - Anand et al., 19 Aug 2026) in Section “Fixing the renormalization scale” (label sec:mu), near the end of the subsection

And finally, an important open question is whether the Noether charges associated with these supertranslation modes can account for the microscopic degrees of freedom responsible for black-hole entropy. More generally, it remains unclear how the infinite-dimensional horizon symmetry structure is encoded in the thermodynamic properties of evolving black holes.

— Near-Horizon BMS Symmetry and Implications on Black Hole Entropy  (2608.26725 - Ghosh et al., 27 Aug 2026) in Section 1, Introduction, enumerated list (fourth item)

One of the main problems in black hole physics is to find its statistical-mechanical foundation; that is, to define the internal degrees of freedom, find the corresponding density matrix, and establish the relation between the thermodynamic and statistical-mechanical definitions such that $S{TD}_{gr}=S{SM}$. While there has been progress in various models, this remains an open problem.

— Entanglement entropy of black holes from the first law of thermodynamics  (2610.11777 - Diakonov et al., 8 Oct 2026) in Section 1, Introduction

Despite these progresses, a complete microscopic description of the entropy of the Schwarzschild BH remains an open problem, for a review see

— Bound States Inside the Horizon and Black Hole Entropy  (2610.21426 - Firouzjahi, 15 Oct 2026) in Section 1, Introduction

We denote the total number of massless species by $N$ but we do not know the exact value of $N$.

— Bound States Inside the Horizon and Black Hole Entropy  (2610.21426 - Firouzjahi, 15 Oct 2026) in Section 3, Microstates Counting