Brans-Dicke theory in Bondi-Sachs form: Asymptotically flat solutions, asymptotic symmetries, and gravitational-wave memory effects
Brans-Dicke theory in Bondi-Sachs form: Asymptotically flat solutions, asymptotic symmetries, and gravitational-wave memory effects
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DOI：
10.1103/physrevd.103.104026
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发表时间：
2020-07
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影响因子：
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通讯作者：
S. Tahura;D. Nichols;A. Saffer;L. Stein;Kent Yagi
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文献类型：
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作者：
S. Tahura;D. Nichols;A. Saffer;L. Stein;Kent Yagi
引力波记忆效应通过其对自由下落的观测者的独特影响而被识别：在波的爆发经过它们的位置之后，记忆效应可以引起观测者的持久相对位移。这些效应与引力和其他无质量场论的红外性质密切相关，包括它们的渐近对称性和守恒量。在本文中，我们调查的记忆效应，对称性，并在布朗-迪克理论守恒量之间的联系。我们计算场方程在邦迪坐标，我们定义了一组边界条件，代表渐近平坦的解决方案在这种情况下。接下来，我们导出了这些时空的渐近对称群，我们发现它与广义相对论中的Bondi-Metzner-Sachs群相同。因为在Brans-Dicke理论中引力波存在一个额外的极化，我们计算了与这个额外极化相关的记忆效应（所谓的“呼吸”模式）。这种呼吸模式使一圈自由下落的观察者产生均匀的膨胀（或收缩）。在这些呼吸引力波经过观测者的位置后，有两个额外的记忆效应取决于它们的初始位移和相对速度。这些额外的记忆效应似乎都与渐近对称性或守恒量无关;相反，它们是由标量场和引力波爆发前后的非辐射区域的性质决定的。我们讨论了这些区域的属性，以支持非平凡的呼吸模式类型的记忆效应。
Gravitational-wave memory effects are identified by their distinctive effects on families of freely falling observers: after a burst of waves pass by their locations, memory effects can cause lasting relative displacements of the observers. These effects are closely related to the infrared properties of gravity and other massless field theories, including their asymptotic symmetries and conserved quantities. In this paper, we investigate the connection between memory effects, symmetries, and conserved quantities in Brans-Dicke theory. We compute the field equations in Bondi coordinates, and we define a set of boundary conditions that represent asymptotically flat solutions in this context. Next, we derive the asymptotic symmetry group of these spacetimes, and we find that it is the same as the Bondi-Metzner-Sachs group in general relativity. Because there is an additional polarization of gravitational waves in Brans-Dicke theory, we compute the memory effects associated with this extra polarization (the so-called "breathing" mode). This breathing mode produces a uniform expansion (or contraction) of a ring of freely falling observers. After these breathing gravitational waves pass by the observers' locations, there are two additional memory effects that depend on their initial displacements and relative velocities. Neither of these additional memory effects seems to be related to asymptotic symmetries or conserved quantities; rather, they are determined by the properties of the nonradiative region before and after the bursts of the scalar field and the gravitational waves. We discuss the properties of these regions necessary to support nontrivial breathing-mode-type memory effects.