Fermion Fields in BTZ Black Hole Space-Time and Entanglement Entropy

Dharm Veer Singh,Sanjay Siwach

doi:10.1155/2015/528762

Abstract

We study the entanglement entropy of fermion fields in BTZ black hole space-time and calculate prefactor of the leading and subleading terms and logarithmic divergence term of the entropy using the discretized model. The leading term is the standard Bekenstein-Hawking area law and subleading term corresponds to first quantum corrections in black hole entropy. We also investigate the corrections to entanglement entropy for massive fermion fields in BTZ space-time. The mass term does not affect the area law.

Highlights

The laws of black hole thermodynamics capture the essential features of macroscopic description of black holes in general theory of relativity
These correlations give an area law (entanglement entropy proportional to the area of entangling surface divided by the cutoff (ε)) and the subleading term in the entanglement entropy contains useful cutoff independent information about the quantum corrections
Since the fermion correlator appearing in the entanglement entropy formula is related to Mij, the matrix appearing in the Hamiltonian, for the general case the entropy of the system is given by a sum over the angular momentum “m.” We diagonalize the correlation matrix and calculate the entanglement entropy, which can be expressed as

Summary

Introduction

The laws of black hole thermodynamics capture the essential features of macroscopic description of black holes in general theory of relativity. The entanglement entropy is defined by the von Neumann entropy relation (SA = −trA[ρA ln ρA]), where ρA is the reduced density matrix of the system A and is dominated by short range correlations across the entangling surface. These correlations give an area law (entanglement entropy proportional to the area of entangling surface divided by the cutoff (ε)) and the subleading term in the entanglement entropy contains useful cutoff independent information about the quantum corrections. We consider the massive fermion fields in BTZ black hole space-time and calculate the entanglement entropy.

Fermions in BTZ Black Hole Space-Time

Numerical Estimation of Entropy

Entanglement Entropy in Free Massive Theory

Results and Conclusion

Dirac Equation in BTZ Black Hole Background

A Model of Entanglement Entropy for Fermion Fields