Gravitational waves propagation in nondynamical Chern–Simons gravity

Abstract

We investigate the propagation of gravitational waves in linearized Chern–Simons (CS) modified gravity by considering two nondynamical models for the coupling field [Formula: see text]: (i) a domain wall and (ii) a surface layer of [Formula: see text], motivated by their relevance in condensed matter physics. We demonstrate that the metric and its first derivative become discontinuous for a domain wall of [Formula: see text], 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 [Formula: see text] 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.