A note on the pp-wave solution of Minimal Massive 3D Gravity coupled with Maxwell-Chern-Simons theory

TL;DR

This paper investigates $pp$-wave solutions in Minimal Massive 3D Gravity coupled with Maxwell-Chern-Simons theory, revealing conditions for solutions and constructing associated conserved charges.

Contribution

It identifies specific conditions for $pp$-wave solutions in MMG coupled with Maxwell-Chern-Simons theory and computes their Noether charges.

Findings

Existence of $pp$-wave solutions under anti-self duality conditions.

Explicit construction of Noether charges for these solutions.

Insight into the coupling effects in MMG with Maxwell-Chern-Simons theory.

Abstract

In this work, we examine a family of $pp$-wave solutions of Minimal Massive 3d Gravity (MMG) minimally coupled with the Maxwell-Chern-Simons theory. An elaborate investigation of the field equations shows that the theory admits $pp$-wave solutions provided that there exist an anti-self duality relation between the electric and the magnetic components of the Maxwell 2-form field. By employing Noether-Wald formalism, we also construct Noether charges of the theory within exterior algebra formalism.