General Logarithmic Corrections to Black Hole Entropy

TL;DR

This work shows that leading entropy corrections for black holes, due to small thermal fluctuations around equilibrium, are universally logarithmic and take the form ${\cal S} = S_0 - \frac{1}{2} \ln(C T^2) + \cdots$ with $S_0$ the Bekenstein–Hawking entropy and $C$ the specific heat. The authors compute explicit coefficients for BTZ, AdS Schwarzschild, and Reissner–Nordström black holes, finding $-\tfrac{3}{2}$, $-\tfrac{d}{2(d-2)}$, and $-\tfrac{d-4}{2(d-2)}$ multiplying $\ln S_0$ in appropriate regimes, respectively, while near-extremality or instability can invalidate the canonical-fluctuation analysis. They further show that an exact entropy function $S(\beta)$ inspired by conformal field theory yields identical leading corrections, reinforcing a potential universal microscopic origin. The results illuminate how negative cosmological constant can stabilize the canonical ensemble and highlight connections to holographic viewpoints and CFT-driven entropy counting across a broad class of black holes.

Abstract

We compute leading order corrections to the entropy of any thermodynamic system due to small statistical fluctuations around equilibrium. When applied to black holes, these corrections are shown to be of the form $-k\ln(Area)$. For BTZ black holes, $k=3/2$, as found earlier. We extend the result to anti-de Sitter Schwarzschild and Reissner-Nordstrom black holes in arbitrary dimensions. Finally we examine the role of conformal field theory in black hole entropy and its corrections.