Asymptotically simple spacetimes and mass loss due to gravitational waves

Abstract

The cosmological constant Λ used to be a freedom in Einstein's theory of general relativity, where one had a proclivity to set it to zero purely for convenience. The signs of Λ or Λ being zero would describe universes with different properties. For instance, the conformal structure of spacetime directly depends on Λ: null infinity I is a spacelike, null, or timelike hypersurface, if Λ > 0, Λ = 0, or Λ < 0, respectively. Recent observations of distant supernovae have taught us that our universe expands at an accelerated rate, and this can be accounted for by choosing Λ > 0 in Einstein's theory of general relativity. A quantity that depends on the conformal structure of spacetime, especially on the nature of I, is the Bondi mass which in turn dictates the mass loss of an isolated gravitating system due to energy carried away by gravitational waves. This problem of extending the Bondi mass to a universe with Λ > 0 has spawned intense research activity over the past several years. Some aspects include a closer inspection on the conformal properties, working with linearisation, attempts using a Hamiltonian formulation based on "linearised" asymptotic symmetries, as well as obtaining the general asymptotic solutions of de Sitter-like spacetimes. We consolidate on the progress thus far from the various approaches that have been undertaken, as well as discuss the current open problems and possible directions in this area.

Bondi mass with a cosmological constant

“…The presence of such a volume integral would be perceived as a significant departure from the asymptotically flat case. Unfortunately, one faces formidable (but hopefully not irreconcilable) difficulty in attempting to pin down an exact notion of the Bondi mass when Λ = 0, because this Λ destroys the asymptotic symmetries which formed the concrete basis for a Hamiltonian treatment of the Bondi mass when Λ = 0 [12]. A ramification of this is the ambiguity in definitively defining the Bondi mass, as demonstrated by the undesirable freedom for moving terms around in Eq.…”

A review of total energy–momenta in GR with a positive cosmological constant

“…However, this proposed new expression depends not only on the instantaneous state of the physical system at u, but on the whole history of the system until u. A summary of the results of the investigations of Saw prior to [73] is given in [71,72].…”

Using gravitational wave to test general relativity

“…宇宙学常数如何影响 引力波的产生以及相关的引力波实验探测是个有趣的 问题. 目前该问题还在研究当中 [43] . Ashtekar等人 [44][45][46][47] 认为Bondi原始的边界条件在存在宇宙学常数的情况 下需要改变, 并研究了不同边界条件对引力波行为的 影响.…”