Asymptotic analysis of Chern-Simons modified gravity and its memory effects

Abstract

We study the asymptotically flat spacetime in Chern-Simons modified gravity and then gravitational memory effects are considered in this work. If the Chern-Simons scalar does not directly couple with the ordinary matter fields, there are also displacement, spin, and center-of-mass memory effects as in general relativity. This is because the term of the action that violates the parity invariance is linear in the scalar field but quadratic in the curvature tensor. This results in the parity violation occurring at the higher orders in the inverse luminosity radius. Although there exists the Chern-Simons scalar field, interferometers, pulsar timing arrays, and the Gaia mission are incapable of detecting its polarization, so the scalar field does not induce any new memory effects that can be detected by interferometers or pulsar timing arrays. The asymptotic symmetry group is also the extended Bondi-Metzner-Sachs group. The constraints on the memory effects excited by the tensor modes are obtained as well.