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 (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.

Scale invariant Einstein–Cartan theory in three dimensions

“…Correspondingly in three-dimensions the bare Einstein's general relativity is not a dynamical theory. Therefore there is a wide literature on modified general relativity in three dimensions [1][2][3][4][5][6][7][8][9].…”