Generalized Gravitational Entropy of Interacting Scalar Field and Maxwell Field

TL;DR

This paper extends the concept of generalized gravitational entropy to interacting scalar and Maxwell fields within BTZ geometry, providing exact solutions and analyzing backreaction effects on horizon area.

Contribution

It introduces a method to compute generalized gravitational entropy for interacting fields and examines backreaction effects, advancing understanding of entropy in complex field systems.

Findings

Exact solution for Maxwell field wave equation

Analytic value of generalized gravitational entropy obtained

Backreaction effects on horizon area analyzed

Abstract

The generalized gravitational entropy proposed by Lewkowycz and Maldacena in recent is extended to the interacting real scalar field and Maxwell field system. Using the BTZ geometry we first investigate the case of free real scalar field and then show a possible way to calculate the entropy of the interacting scalar field. Next, we investigate the Maxwell field system. We exactly solve the wave equation and calculate the analytic value of the generalized gravitational entropy. We also use the Einstein equation to find the effect of backreaction of the Maxwell field on the area of horizon. The associated modified area law is consistent with the generalized gravitational entropy.