# Chemical Potential and Charge in Quantum Black Holes

**Authors:** Ana Climent, Roberto Emparan, Robie A. Hennigar  
**arXiv:** [2404.15148](https://arxiv.org/abs/2404.15148)  
**Date:** 2024-04-23  
**Summary page:** https://www.summarizepaper.com/en/paper/2404.15148v1/

## Key points

- Authors Ana Climent, Roberto Emparan, and Robie A. Hennigar study systems in $2+1$ dimensions involving defects sourcing electric charges or magnetic fluxes of a $U(1)$ field.
- They use holography to investigate how these defects impact quantum conformal fields.
- The researchers explore concealing defects within the event horizon of a black hole, where they influence quantum fields outside.
- By extending solutions to braneworld holography, they uncover the non-linear backreaction of quantum fields on both defect and black hole backgrounds.
- This analysis leads to the emergence of quantum charged point particles and black holes with unique characteristics.
- Charged quantum black holes show significant deviations from classically charged BTZ black holes due to superior asymptotic behavior of the quantum-induced electromagnetic field in $2+1$ dimensions.
- A novel class of (near-)extremal charged quantum black holes featuring AdS$_2$ throats is discovered.
- This discovery opens new avenues for exploring interplay between quantum effects, charges, and black hole dynamics in lower-dimensional spacetimes.

## Summary

In their paper titled "Chemical Potential and Charge in Quantum Black Holes," authors Ana Climent, Roberto Emparan, and Robie A. Hennigar delve into the study of systems in $2+1$ dimensions that involve defects sourcing electric charges or magnetic fluxes of a $U(1)$ field. Utilizing holography, they investigate how these defects impact quantum conformal fields. The researchers also explore the intriguing scenario of concealing these defects within the event horizon of a black hole, where they continue to influence the quantum fields outside. By extending their solutions to braneworld holography, Climent, Emparan, and Hennigar uncover the non-linear backreaction of the quantum fields on both the defect and black hole backgrounds. This analysis leads to the emergence of quantum charged point particles and black holes with unique characteristics. Notably, the charged quantum black holes exhibit significant deviations from classically charged BTZ black holes due to the superior asymptotic behavior of the quantum-induced electromagnetic field in $2+1$ dimensions compared to its classical counterpart. Furthermore, their construction unveils a novel class of (near-)extremal charged quantum black holes featuring AdS$_2$ throats. This discovery opens up new avenues for exploring the intricate interplay between quantum effects, charges, and black hole dynamics in lower-dimensional spacetimes. The comprehensive investigation presented by Climent et al. sheds light on the rich phenomenology arising from incorporating quantum considerations into the study of black hole physics and defect interactions within holographic frameworks.