Mass loss due to gravitational waves with Λ &gt; 0

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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.

“…For simplicity, we could consider the axisymmetric case given by Eq. (35). This would lead to a set of PDEs, which unfortunately, we are unable to analytically solve.…”

Section: Asymptotically De Sitter Spacetimesmentioning

confidence: 98%

Asymptotically simple spacetimes and mass loss due to gravitational waves

Saw

2017

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“…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].…”

Section: Mass-loss and The Solution Of The Np Equationsmentioning

confidence: 99%

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

Szabados

Paul

2019

A review is given of the various approaches to and expressions for total energymomentum and mass in the presence of a positive cosmological constant in Einstein's field equations, together with a discussion of the key conceptual questions, main ideas and techniques behind them. * Dedicated to our friend, Jörg Frauendiener, on the occasion of his 60th birthday.Ach, wie schön muss sich's ergehen, Dort in Newmans Himmelsraum. Und Lichtkugeln auf den Höhen -O wie lab'n sie meinen Traum ! from Ein theoretisch-physikalischer Schiller-Traum by N. V. Mitskievitch future of the point with Cartesian coordinates (τ, 0, 0, 0). All the leaves of this latter foliation intersect the future null infinity at one and the same cut u = τ , rather than providing a foliation of the null infinity (see Fig. 1.iii.).3 This can be proved, given certain causality assumptions; see [16].

“…Recently, the behaviour of empty asymptotically (anti-)de Sitter spacetimes has been studied [6], and further extended to contain Maxwell fields [7] (see also [8][9][10] [11]). These took the approach of exclusively studying the physical spacetime, i.e.…”

Section: Introductionmentioning

confidence: 99%

“…with no involvement of spacetime compactification): (1) The peeling property of the Weyl spinor is guaranteed. In the case where there are Maxwell fields present, the peeling properties of both Weyl and Maxwell spinors similarly hold, if the leading order term of the spin coefficient ρ when expanded as inverse powers of r (where r is the usual spherical radial coordinate, and r → ∞ is null infinity, I) has coefficient −1.(2) In the absence of gravitational radiation (a conformally flat I), the group of asymptotic symmetries is trivial, with no room for supertranslations.Recently, the behaviour of empty asymptotically (anti-)de Sitter spacetimes has been studied [6], and further extended to contain Maxwell fields [7] (see also [8][9][10] [11]). These took the approach of exclusively studying the physical spacetime, i.e.…”

mentioning

confidence: 99%

Peeling property and asymptotic symmetries with a cosmological constant

Saw

Thun²

2020

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This paper establishes two things in an asymptotically (anti-)de Sitter spacetime, by direct computations in the physical spacetime (i.e. with no involvement of spacetime compactification): (1) The peeling property of the Weyl spinor is guaranteed. In the case where there are Maxwell fields present, the peeling properties of both Weyl and Maxwell spinors similarly hold, if the leading order term of the spin coefficient ρ when expanded as inverse powers of r (where r is the usual spherical radial coordinate, and r → ∞ is null infinity, I) has coefficient −1.(2) In the absence of gravitational radiation (a conformally flat I), the group of asymptotic symmetries is trivial, with no room for supertranslations.Recently, the behaviour of empty asymptotically (anti-)de Sitter spacetimes has been studied [6], and further extended to contain Maxwell fields [7] (see also [8][9][10] [11]). These took the approach of exclusively studying the physical spacetime, i.e. no conformal rescaling was explicitly made in deriving those asymptotic solutions. In accordance to the case for asymptotically flat spacetimes, the imposed condition Ψ 0 = O(r −5 ) leads to the expected peeling property for the Weyl spinor and a similar condition on the dyad component of the Maxwell spinor φ 0 = O(r −3 ) yields the analogous peeling behaviour for the Maxwell fields.These peeling properties of Ψ n and φ m (where m = 0, 1, 2) with a non-zero cosmological constant should not be surprising, as the peeling property for the Weyl spinor has been proven for (weakly) asymptotically simple spacetimes that do include asymptotically (anti-)de Sitter spacetimes [12][13][14]. This follows from admitting a smooth conformal compactifiability and working with a conformally compactified version of the spacetime, involving spinors.The driving motivation in Ref. [6] was to generalise the notion of the Bondi mass of an isolated gravitating system, and the mass loss due to energy carried away by gravitational waves with a positive cosmological constant, Λ > 0 -since we now know that our universe expands at an accelerated rate (which is well described by Einstein's theory with Λ > 0).Although Bondi et al. led the initial breakthrough to this problem for the asymptotically flat case [2,15], the mass-loss formula for Λ = 0 could also be obtained using the Newman-