A note on the pp-wave solution of minimal massive 3D gravity coupled with Maxwell–Chern–Simons theory

Abstract

In this work, we examine a family of pp-wave solutions of minimal massive 3D gravity 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 two-form field. By employing Noether–Wald formalism, we also construct Noether charges of the theory within exterior algebra formalism.