Gravitational waves from isolated systems: The phantom menace of a positive Λ

Primary motivation: conceptual. Some 100 Years have passed since Einstein's discovery quadrupole formula and some 50 years since the Bondi-Penrose framework. For 15 years, we have known that the accelerated expansion of the universe is best explained by a positive Λ. Now, numerical relativists, observers and experimentalists have taken us to the dawn of the new era of gravitational wave science. So it is high time that we have a firm theoretical framework describing gravitational waves in GR with A > 0. (Recall the confusion about reality of gravitational waves during the first 50 years of GR!) • The issue of this extension has been open so long because inclusion of A, however small, introduces novel conceptual issues both in full theory and in the linear approximation. These arise because the asymptotic space-time structure changes non-trivially: I+ is space-like rather than null. Hence problems persist if Λ were to be replaced by some other form of 'dark energy' so long as the accelerated expansion continues to the future. • Stability of I+ for Λ > 0 was established in a pioneering work by Friedrich in 1991. But the problem of extracting physical information has been open: Bondi news; energy, momentum and angular momentum 2-sphere integrals; expressions of fluxes of these quantities; relation between the radiated power to properties of sources in the weak field, slow motion limit,⋯ Even a tiny A casts a long shadow! • These issues have now been resolved in the weak field limit: Post de Sitter, first post-Newtonian approximation. A priori it is not obvious that tiny Λ can only make negligible corrections because the limit is discontinuous in important ways: I⁺changes its character. But detailed analysis provides systematic ways of calculating the 'error' terms and shows why and how the concerns can be by-passed. For full, non-linear GR, well-developed strategies but further work is needed. • Open issues: Examples: (i) Is the analog of Bondi-energy 2-sphere integral positive if the matter satisfies energy conditions and H^-is a weakly isolated horizon? Recall the importance of the positive energy theorem in geometric analysis. (ii) Is the radiated flux positive (since there is no energy flux across H^-) as in the new quadrupole formula? If not, there would be gravitational instabilities. Comment: Definitions of de Sitter momenta of Abbott & Deser; Kelley & Marolf; Chrusciel, Jezierski & Kijowski;⋯ refer to i°. Positive energy theorems of Kastor & Traschen; Luo, Xie and Zhang also refer to i° and, furthermore, a conformal Killing field in de Sitter, which is not an asymptotic symmetry. Szabodas & Tod: Positive charge but interpretation unclear. (Figure presened) Conceptual problems in specifying asymptotic Hilbert spaces for the Hawking radiation resolved in the new scenario: incoming states can be specified on H^-and outgoing on H⁺, even allowing for back-reaction due to outgoing radiation.