theoretical physics

Horizon Microstructure Thermodynamics in AdS Black Holes: Smarr-Consistent Excitation Enthalpy

arXiv:2607.13824

summary

The paper models a four‑dimensional AdS black hole horizon as a collection of microscopic sites, using combinatorial counting to recover the Bekenstein–Hawking entropy and derive an extended thermodynamic description with a chemical potential and Smarr‑consistent excitation enthalpy.

Abstract

In this work we formulate a horizon-microstructure description of four-dimensional AdS black holes in which a horizon of area $A$ is resolved into $N = A / a_{p}$ microscopic sites and $N$ occupied horizon sites. The central result is that the combinatorics of this partially occupied horizon sector yields the entropy directly: in the finite-filling regime the leading term is proportional to the area, and the maximal-entropy filling reproduces the Bekenstein--Hawking law with $a_{p} = 4 ln 2 ℓ_{p}^{2}$ . Subleading corrections include a subtractive logarithmic term and an inverse-area expansion. We then show that this partially occupied regime admits a thermodynamic justification from an extended first law with chemical potential $I^¼$ , a Smarr-consistent excitation enthalpy $I^´ M (A, P, N)$ , and an AdS control parameter $u = P S$ . In this interpretation, the combinatorics provides the dominant horizon entropy, while the thermodynamic sector supplies a dressing that selects the equilibrium filling and assigns a finite excitation cost to departures from a reference partially occupied configuration.

Topics & keywords

#black hole thermodynamics #ads spacetime #horizon microstructure #entropy corrections #extended phase spaceBekenstein-Hawking entropychemical potentialexcitation enthalpylogarithmic correctionsarea quantizationSmarr relation