Gravitational waves from isolated systems: Surprising consequences of a positive cosmological constant

There is a deep tension between the well-developed theory of gravitational waves from isolated systems and the presence of a positive cosmological constant $\mathrm{\Lambda }$, however tiny. In particular, even the post-Newtonian quadrupole formula, derived by Einstein in 1918, has not been generalized to include a positive $\mathrm{\Lambda }$. We first explain the principal difficulties and then show that it is possible to overcome them in the weak field limit. These results also provide concrete hints for constructing the $\mathrm{\Lambda }>0$ generalization of the Bondi-Sachs framework for full, non-linear general relativity.