Entanglement Thermodynamics of the Generalized Charged BTZ Black Hole

TL;DR

This paper explores the entanglement entropy of the generalized charged BTZ black hole using holographic methods, establishing a first law-like relation and renormalizing the energy tensor within the AdS/CFT framework.

Contribution

It introduces a detailed holographic analysis of entanglement entropy for charged BTZ black holes, including second-order variations and energy tensor renormalization.

Findings

Derived a first law-like relation between entanglement entropy and energy variations.

Calculated counterterms for energy tensor renormalization.

Extended the holographic entanglement entropy framework to charged BTZ black holes.

Abstract

In this paper, we investigate the entanglement entropy for the generalized charged BTZ black hole through the $AdS_{3}/CFT_{2}$ correspondence. Using the holographic description of the entanglement entropy for the strip-subsystem in boundary $CFT_{2}$, we will find the first law-like relation between the variation of holographic entanglement entropy and the variation of energy of the subsystem in terms of the mass and the electric charge up to the second order. We also obtain appropriate counterterms to renormalize the energy tensor associated with the bulk on-shell actions.