Propagation of gravitational waves in teleparallel gravity theories

We investigate the propagation of gravitational waves in the most general teleparallel gravity model with second order field equations as perturbations around the Minkowski background. We argue that in this case the most general Lagrangian at the first nonvanishing order of the perturbations is given by a linear combination of quadratic invariants and hence coincides with the well-known new general relativity model. We derive the linearized field equations and analyze them using the principal polynomial and the Newman-Penrose formalism. We demonstrate that all gravitational wave modes propagate at the speed of light, and there are up to six possible polarizations. We show that two tensorial modes of general relativity are always present, and the number of extra polarizations depends on the free parameters of the new general relativity model.

Figure 1

Visualization of the parameter space using polar coordinates. The radial axis shows the zenith angle $\theta$, whereas the (circular) polar axis shows the azimuth angle $\varphi$, following the definition (38). Blue points: $2c_1+c_2=c_3=0$, class ${\mathrm{II}}_6$, 6 polarizations. Green line: $2c_1+c_2+c_3\ne 0,2c_1(c_2+c_3)+c_2^2=0$, class ${\mathrm{III}}_5$, 5 polarizations. White area: $2c_1(c_2+c_3)+c_2^2\ne 0,2c_1+c_2+c_3\ne 0$, class ${\mathrm{N}}_3$, 3 polarizations. Red line: $2c_1+c_2+c_3=0,c_3\ne 0$, class ${\mathrm{N}}_2$, 2 polarizations.