Holographic Central Charge Effects on Black Hole Thermodynamics and Quantum Information

TL;DR

This paper explores how the holographic central charge influences black hole thermodynamics and quantum information, revealing different behaviors for large and small central charges and demonstrating the recovery of the Page curve using the island formula.

Contribution

It establishes the role of the holographic central charge in connecting boundary CFT properties to black hole thermodynamics and quantum information, including the impact on the Page curve and unitarity.

Findings

Large central charge leads to classical black hole behavior with phase transitions.

Small central charge results in stable black holes with reduced entropy.

The island formula recovers the Page curve, with entropy slope determined by the central charge.

Abstract

In this paper, based on the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, we highlight the fundamental role of the holographic central charge in connecting the boundary theory to quantum information, black hole thermodynamics, and the nature of gravity in the bulk. We establish that the large central charge of the boundary conformal field theory corresponds to classical gravity, while a small central charge corresponds to quantum gravity described by Loop Quantum Gravity. In addition, we study the thermodynamic behavior of AdS-Schwarzschild black holes for both large and small central charges. For large central charge, the classical AdS-Schwarzschild black holes have two phases: unstable small black holes and stable large black holes. Conversely, for small central charge, black holes are stable, and their entropy is smaller than that of classical black holes. To explore the influence of the boundary central charge on the information loss paradox, we use the island formula to recover the Page curve. We find that before the Page time, the entanglement entropy of Hawking radiation increases with time, and its slope is determined by the central charge of the boundary theory. After the Page time, the island inside black holes emerges, and the unitarity of black hole evaporation is restored, yielding a constant entropy consistent with the Page curve. This entanglement entropy, i.e. after the Page time, depends on the Bekenstein-Hawking entropy and includes a logarithmic correction related to the central charge.