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

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.

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