Gravitational radiation condition at infinity with a positive cosmological constant

Abstract

Gravitational waves have been directly detected and astronomical observations indicate that our Universe has a positive cosmological constant Λ. Nevertheless, a theoretical gaugeinvariant notion of gravitational waves arriving at infinity (escaping from the space-time) in the presence of a positive Λ has been elusive. We find the answer to this long-standing gravitational puzzle, and present a geometric, gauge-invariant radiation condition at infinity.

Poynting vector, super-Poynting vector, and principal observers in electromagnetism and general relativity

“…It should also (being an energy current) generate a 'Magnus'-like force on spinning test bodies [62]. The super-Poynting vector is likewise believed to accompany gravitational radiation [11][12][13][14][15][16], and, in stationary settings such as those in figure 6, where (similarly to its EM counterpart) it circulates around in closed loops, observable consequences have been sought, namely an attempted link to frame-dragging 22 [63]. 21 Indeed p a looks very strange sometimes.…”

“…ϑ = π 2 , and retrieve from (133) and ( 134) that (87) and ( 88) is valid, such that ρ g increases with |ϕ| = ψ Σ ; for i = 1(u 2 = u 3 = 0), however, we have ψ Σ = 0: for all values of ϕ = γ the observers (132) with i = 1 belong to Σ, are thus principal (P a = 0), and have the same minimal super-energy density ρ 1 g (ϕ) = ξ, in agreement with characterizations ( j) and (d) of principal observers. This amends the statement at the end of section 5 of [26] when applied to Petrov type D. 15 In the Petrov type I case the special observers (132) may be characterized as follows. For an arbitrary observer u a given by (97) the orthogonal eigendirections of the endomorphism Q associated to an observer u a are generated by the three vectors x a i given in (99).…”

“…The non-null case I F = 0 remains. Here we can normalize F ab to the unitary self-dual bivector X ab = F ab / √ I F , where √ I F is one of the two square roots of I F given by (2) with z = I F ; by (15) a restricted orthonormal tetrad (e a 0 , e a i ) exists such that…”

“…Landau-Lifshitz's) can be found in the literature [3,[8][9][10]. It is moreover believed that gravitational radiation is accompanied by a super-Poynting vector [11][12][13][14][15][16]; in the linear regime, this is clearly suggested by Matte's equations [17], and, recently, a relationship with the quasi-local wave energy flux has been put forth [16]; in the exact theory, it has also recently been shown [14] that a variant of it yields a characterization of the presence of gravitational radiation equivalent to the classical one, given by the News tensor. This fosters the interest in studying the observers relative to which the super-Poynting vector vanishes, and led to the proposal, inspired by the electromagnetic analogy, of the non-existence of such observers at a given point as a criterion for 'intrinsic radiation' [12].…”