Gravitational radiation condition at infinity with a positive cosmological constant

Gravitational waves have been directly detected and astronomical observations indicate that our Universe has a positive cosmological constant $\mathrm{\Lambda }$. Nevertheless, a theoretical gauge-invariant notion of gravitational waves arriving at infinity (escaping from the space-time) in the presence of a positive $\mathrm{\Lambda }$ has been elusive. We find the answer to this long-standing gravitational puzzle and present a geometric, gauge-invariant radiation condition at infinity.

Figure 1

Asymptotic canonical superenergy for the C-metric with a choice of parameters $\mathrm{\Lambda }=1$, $\alpha =m=1/4$. The solid line represents the norm of the canonical super-Poynting vector of Eq. (24); observe that it is nonvanishing in the whole range of the coordinate $p$—excluding the conical singularities—indicating the presence of gravitational radiation there. The dashed line corresponds to the canonical superenergy density of Eq. (25) that, of course, is nonvanishing.