Asymptotically simple spacetimes and mass loss due to gravitational waves
Abstract
The cosmological constant ΛΛ used to be a freedom in Einstein’s theory of general relativity (GR), where one had a proclivity to set it to zero purely for convenience. The signs of ΛΛ or ΛΛ being zero would describe universes with different properties. For instance, the conformal structure of spacetime directly depends on ΛΛ: 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 GR. 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 linearization, attempts using a Hamiltonian formulation based on “linearized” 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.
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