Gravitational waves in a minimal gravitational SME

TL;DR

This work analyzes gravitational waves within the minimal gravitational SME by examining linearized gravity around Minkowski space and focusing on the transverse-traceless tensor sector. The authors derive the modified dispersion and causal structure via the retarded Green function, showing that Lorentz-violating effects introduce a velocity shift $v_{\pm}=1-\mathring{k}^{(4)}_{(I)}$ that manifests as a phase modification in the waveform without altering amplitude or polarization. Gravitational radiation from a binary black-hole system is shown to follow the standard quadrupole form with the same polarization content, except for the retarded time replaced by $t_r^{(\pm)}=t-r/v_{\pm}$. Phenomenological bounds on the isotropic coefficient $\mathring{k}^{(4)}_{(I)}$ are obtained from GW observations, yielding $|\mathring{k}^{(4)}_{(I)}| \lesssim 10^{-15}$, thereby constraining deviations from luminal propagation in the minimal sector.

Abstract

In this work, we investigate the generation and propagation of gravitational waves within a minimal gravitational SME (Standard Model Extension). Starting from the modified graviton dispersion relation derived in the linearized gravity sector, we analyze the polarization properties of gravitational waves in the transverse-traceless tensor sector. We then construct the retarded Green function associated with the Lorentz-violating wave operator, explicitly verifying the causal structure of the theory and identifying the modified propagation speeds of the tensorial modes. In addition, we study the source-induced emission of gravitational waves from a binary black-hole system. We show that the gravitational waveform preserves the standard quadrupolar amplitude and polarization structure, while Lorentz-violating effects enter exclusively through a modification of the retarded time. As a result, the spatial components of the metric perturbation $h_{ij}(t,r)$ acquire a phase shift determined by the SME coefficients. Finally, we estimate phenomenological bounds to the model under consideration.

Figures (3)

• Figure 1: Binary black-hole configuration in the center-of-mass frame. Two compact masses, $m_1$ and $m_2$, orbit within the $xy$ plane with orbital radii $r_1$ and $r_2$.
• Figure 2: The spatial components $h_{xx}^{(\pm)}(t,r)$ (up panel) and $h_{yy}^{(\pm)}(t,r)$ (down panel) are shown as functions of time $t$ for several representative values of the propagation speed $v_{\pm}$. For reference, the standard general relativity result, corresponding to $v_{\pm}=1$, is also displayed for comparison.
• Figure 3: The joint evolution of the components $h_{yx}^{(\pm)}(t,r)$ and $h_{xx}^{(\pm)}(t,r)$ is illustrated through parametric curves evaluated for different values of the propagation speed $v_{\pm}$. The standard general relativity behavior, recovered when $v_{\pm}=1$, is included for reference.