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

TL;DR

This paper explores the challenges and solutions for understanding gravitational waves from isolated systems in the presence of a positive cosmological constant, offering insights into extending classical frameworks to include $\, ext{Lambda}>0$.

Contribution

It identifies key difficulties and demonstrates how to generalize gravitational wave theory to incorporate a positive cosmological constant in the weak field limit.

Findings

Overcomes principal difficulties in including positive $\, ext{Lambda}$ in gravitational wave theory.

Provides concrete hints for extending the Bondi-Sachs framework to $\, ext{Lambda}>0$.

Suggests possible pathways for full non-linear general relativity generalizations.

Abstract

There is a deep tension between the well-developed theory of gravitational waves from isolated systems and the presence of a positive cosmological constant $\Lambda$, however tiny. In particular, even the post-Newtonian quadrupole formula, derived by Einstein in 1918, has not been generalized to include a positive $\Lambda$. 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 $\Lambda >0$ generalization of the Bondi-Sachs framework for full, non-linear general relativity.