Asymptotically simple spacetimes and mass loss due to gravitational waves

Abstract

The cosmological constant $\Lambda$ 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 $\Lambda$ or $\Lambda$ being zero would describe universes with different properties. For instance, the conformal structure of spacetime directly depends on $\Lambda$: null infinity $\mathcal{I}$ is a spacelike, null, or timelike hypersurface, if $\Lambda >0$, $\Lambda =0$, or $\Lambda <0$, 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 $\Lambda >0$ in Einstein's theory of general relativity. A quantity that depends on the conformal structure of spacetime, especially on the nature of $\mathcal{I}$, 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 $\Lambda >0$ 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.

arXiv comment41 pages, 2 figures

References in corpus (26)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• Observation of Gravitational Waves from a Binary Black Hole Merger
• GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence
• The Dynamics of General Relativity
• Precision Measurement of the Casimir Force from 0.1 to 0.9 microns
• Bondi-Sachs Formalism
• Asymptotics with a positive cosmological constant: I. Basic framework
• Asymptotics with a positive cosmological constant: II. Linear fields on de Sitter space-time
• Asymptotics with a positive cosmological constant: III. The quadrupole formula
• Energy of Isolated Systems at Retarded Times as the Null Limit of Quasilocal Energy
• Gravitational waves from isolated systems: Surprising consequences of a positive cosmological constant
• Gravitational waves in a de Sitter universe
• Gravitational Waves from Compact Sources in de Sitter Background
• The cosmological constant and the energy of gravitational radiation
• On the AdS stability problem
• A positive Bondi--type mass in asymptotically de Sitter spacetimes
• Mass-loss of an isolated gravitating system due to energy carried away by gravitational waves with a cosmological constant
• Projective Compactifications and Einstein metrics
• Behaviour of asymptotically electro-$\Lambda$ spacetimes
• Mass loss due to gravitational waves with $\Lambda >0$
• On an integral formula on hypersurfaces in General Relativity
• "Twisted" black holes are unphysical
• Helicalised fractals
• Curved traversable wormholes in (3+1)-dimensional spacetime
• Constructing vacuum spacetimes by generating manifolds of revolution around a curve

Cited by in corpus (4)

• Asymptotic Structure with a positive cosmological constant
• A review of total energy-momenta in GR with a positive cosmological constant
• Bondi mass with a cosmological constant
• Peeling property and asymptotic symmetries with a cosmological constant