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Action integrals for quantum BTZ black holes

Yuanfan Cao, Andrew Svesko

TL;DR

The paper addresses the challenge of quantum backreaction in black hole thermodynamics by embedding (2+1)D quantum BTZ black holes in a four-dimensional AdS bulk with end-of-the-world branes, enabling exact backreaction through braneworld holography. It computes the grand-canonical partition function from the on-shell Euclidean action of accelerating AdS$_4$ C-metric spacetimes reguated by a second ETW brane, deriving the full qBTZ thermodynamics and showing the entropy equals the generalized entropy on the brane, $S^{(3)}_{ ext{gen}}$. The construction is extended to charged, rotating quantum black holes in dS$_3$ and Mink$_3$ via Randall–Sundrum branes, illustrating horizons induced by backreaction in these settings and providing horizon thermodynamics from the same on-shell action. Altogether, this work provides a first-principles derivation of the generalized entropy for exact 3D quantum black holes and establishes a controlled framework for studying backreaction, stability, and quantum Penrose-type bounds within holography.

Abstract

Black holes exactly incorporating quantum matter backreaction effects, namely, quantum black holes, are notoriously difficult to construct, let alone study their horizon thermodynamics. Here, we derive the thermodynamics of three-dimensional charged and rotating quantum black holes via the tree-level gravitational partition function. Specifically, we primarily focus on holographic quantum BTZ black holes, dual to $(3+1)$-dimensional accelerating black holes in anti-de Sitter space that localize on Karch-Randall end-of-the-world (ETW) branes. To derive their horizon thermodynamics, we regulate the bulk Euclidean geometry by adding a second ETW brane at asymptotic spatial infinity. We compute the on-shell action of the complexified accelerating black hole in the grand canonical ensemble and derive the quantum BTZ black hole thermodynamics, where the thermal entropy is equal to the generalized entropy. This provides a first principles derivation of the generalized entropy of three-dimensional quantum black holes. Further, we construct charged and rotating quantum black holes in three-dimensional de Sitter and Minkowski space using Randall-Sundrum ETW branes, and compute their horizon thermodynamics.

Action integrals for quantum BTZ black holes

TL;DR

The paper addresses the challenge of quantum backreaction in black hole thermodynamics by embedding (2+1)D quantum BTZ black holes in a four-dimensional AdS bulk with end-of-the-world branes, enabling exact backreaction through braneworld holography. It computes the grand-canonical partition function from the on-shell Euclidean action of accelerating AdS C-metric spacetimes reguated by a second ETW brane, deriving the full qBTZ thermodynamics and showing the entropy equals the generalized entropy on the brane, . The construction is extended to charged, rotating quantum black holes in dS and Mink via Randall–Sundrum branes, illustrating horizons induced by backreaction in these settings and providing horizon thermodynamics from the same on-shell action. Altogether, this work provides a first-principles derivation of the generalized entropy for exact 3D quantum black holes and establishes a controlled framework for studying backreaction, stability, and quantum Penrose-type bounds within holography.

Abstract

Black holes exactly incorporating quantum matter backreaction effects, namely, quantum black holes, are notoriously difficult to construct, let alone study their horizon thermodynamics. Here, we derive the thermodynamics of three-dimensional charged and rotating quantum black holes via the tree-level gravitational partition function. Specifically, we primarily focus on holographic quantum BTZ black holes, dual to -dimensional accelerating black holes in anti-de Sitter space that localize on Karch-Randall end-of-the-world (ETW) branes. To derive their horizon thermodynamics, we regulate the bulk Euclidean geometry by adding a second ETW brane at asymptotic spatial infinity. We compute the on-shell action of the complexified accelerating black hole in the grand canonical ensemble and derive the quantum BTZ black hole thermodynamics, where the thermal entropy is equal to the generalized entropy. This provides a first principles derivation of the generalized entropy of three-dimensional quantum black holes. Further, we construct charged and rotating quantum black holes in three-dimensional de Sitter and Minkowski space using Randall-Sundrum ETW branes, and compute their horizon thermodynamics.
Paper Structure (15 sections, 177 equations, 1 figure)

This paper contains 15 sections, 177 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Quantum BTZ black holes
  3. Set-up: bulk and brane
  4. Quantum black holes on the brane
  5. Euclidean action of quantum BTZ black holes
  6. General strategy
  7. Regularity of the accelerating black hole and thermal ensembles
  8. Euclidean action
  9. Quantum black hole thermodynamics
  10. Charged and rotating black holes in dS$_{3}$ and Mink$_{3}$
  11. Black holes in dS$_{3}$
  12. Black holes in Mink$_{3}$
  13. Discussion and outlook
  14. Semi-classical and holographically induced gravity
  15. C-metric geometry

Figures (1)

  • Figure 1: Accelerating black hole in AdS$_{4}$. A constant $t$ and $\phi$ slice of the $\text{AdS}_{4}$ C-metric. Conical singularities distort the black hole horizon, giving it a conical shape at one pole where a cosmic string is attached, suspending the black hole away from the center.