# Gravitational waves propagation in nondynamical Chern-Simons gravity

## TL;DR

This paper studies how gravitational waves behave in a modified gravity theory with Chern-Simons terms, revealing discontinuities and boundary effects depending on the model of the coupling field.

## Contribution

It analyzes gravitational wave propagation in nondynamical Chern-Simons gravity with novel boundary conditions and discontinuities, extending understanding of wave behavior in such modified theories.

## Key findings

- Discontinuous metric and derivatives across a domain wall of the coupling field.
- Boundary conditions derived from self-adjoint extensions of the wave operator.
- Reflection and transmission coefficients calculated for different models.

## Abstract

We investigate the propagation of gravitational waves in linearized Chern-Simons (CS) modified gravity by considering two nondynamical models for the coupling field $\theta$: (i) a domain wall and (ii) a surface layer of $\theta$, motivated by their relevance in condensed matter physics. We demonstrate that the metric and its first derivative become discontinuous for a domain wall of $\theta$, and we determine the boundary conditions by realizing that the additional contribution to the wave equation corresponds to one of the self-adjoint extensions of the D'Alembert operator. Nevertheless, such discontinuous metric satisfies the area matching conditions introduced by Barrett. On the other hand, the propagation through a surface layer of $\theta$ behaves similarly to the propagation of electromagnetic waves in CS extended electrodynamics. In both cases we calculate the corresponding reflection and transmission amplitudes. As a consequence of the distributional character of the additional terms in the equations that describe wave propagation, the results obtained for the domain wall are not reproduced when the thickness of the surface layer goes to zero, as one could naively expect.