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arXiv 1506.06152gr-qcastro-ph.COhep-th
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正宇宙学常数的渐近性：II。de Sitter时空中的线性场

Asymptotics with a positive cosmological constant: II. Linear fields on de Sitter space-time

Abhay Ashtekar, Béatrice Bonga, Aruna Kesavan

备注：
22 pages, 4 figures. Added two clarifications in section V (on the use of the Poincaré patch and on the relation with Friedrich's result [19] in full GR). We thank the referee for bringing to our attention Ref [19]. Version to appear in PRD
发表信息：
Phys. Rev. D 92, 044011 (2015)
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摘要：

详细分析了deSitter时空中的线性化引力波，为在完全非线性广义相对论中建立正宇宙学常数的引力辐射理论提供了指导.具体而言：i）在精确理论中，为了将渐近对称群从$\Diff$约化为de Sitter群，通常假设$\scri$的内禀几何是共形平坦的。我们的结果表明，这个条件在物理上是不合理的：ii）我们得到了引力波携带的能量-动量和角动量通量的表达式，这些表达式是用$\scrip$定义的场表示的：iii）我们认为，尽管线性化的引力波的能量一般可以是任意负的，但由物理上合理的源发射的引力波携带正能量;最后iv）我们证明了尽管极限$Λ\to 0$是不连续的（特别是因为$\scri$在极限中将其类空性质变为零），通量公式仍还原为闵可夫斯基时空中的通量公式。

英文摘要：

Linearized gravitational waves in de Sitter space-time are analyzed in detail to obtain guidance for constructing the theory of gravitational radiation in presence of a positive cosmological constant in full, nonlinear general relativity. Specifically: i) In the exact theory, the intrinsic geometry of $\scri$ is often assumed to be conformally flat in order to reduce the asymptotic symmetry group from $\Diff$ to the de Sitter group. Our {results show explicitly} that this condition is physically unreasonable; ii) We obtain expressions of energy-momentum and angular momentum fluxes carried by gravitational waves in terms of fields defined at $\scrip$; iii) We argue that, although energy of linearized gravitational waves can be arbitrarily negative in general, gravitational waves emitted by physically reasonable sources carry positive energy; and, finally iv) We demonstrate that the flux formulas reduce to the familiar ones in Minkowski space-time in spite of the fact that the limit $Λ\to 0$ is discontinuous (since, in particular, $\scri$ changes its space-like character to null in the limit).

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