Brans-Dicke 理论的 Damour-Esposito-Farèse 扩展中的引力波记忆效应
Gravitational-wave memory effects in the Damour-Esposito-Farèse extension of Brans-Dicke theory
AI总结：
本文在 Bondi-Sachs 框架下研究了 Brans-Dicke 理论的 Damour-Esposito-Farèse 扩展中的引力波记忆效应，发现两理论记忆效应差异为二阶小量，难以用于区分理论，但有助于解释数值模拟。
摘要：
引力波记忆效应是应变及其时间积分的持久变化。在 Bondi-Sachs 框架中，可以使用守恒和演化方程在渐近平坦时空中计算这些效应。修正引力理论具有额外的自由度及其自身的渐近演化方程；这些附加场会导致这些理论中的记忆效应与广义相对论中的不同。在本研究中，我们研究了一种被称为 Brans-Dicke 理论的 Damour-Esposito-Farèse 扩展的标量-张量引力理论。我们使用 Bondi-Sachs 框架计算了 Bondi-Sachs 形式的场方程、渐近平坦解以及主导的引力波记忆效应。尽管 Damour-Esposito-Farèse 理论具有 Brans-Dicke 理论中不存在的额外非线性，但这些非线性是次主导效应；因此，这两个理论在超曲面方程、渐近对称性和记忆效应类型的主导（以及部分次主导）解方面具有许多相似之处。这两个理论的质量和角动量方面的守恒方程有所不同，主要是由于标量场演化方程的差异。这导致了在致密双星的准圆旋近期间产生的引力波记忆信号的时间依赖性存在差异。然而，这些差异在这些理论的一个小耦合参数中属于二阶效应，这表明使用记忆效应来区分这两个理论将具有挑战性。尽管如此，我们的结果可用于分析和解释该理论中双星数值相对论模拟的记忆效应。
英文摘要：
Gravitational-wave memory effects are lasting changes in the strain and its time integrals. They can be computed in asymptotically flat spacetimes using the conservation and evolution equations in the Bondi-Sachs framework. Modified theories of gravity have additional degrees of freedom with their own asymptotic evolution equations; these additional fields can produce differences in the memory effects in these theories from those in general relativity. In this work, we study a scalar-tensor theory of gravity known as the Damour-Esposito-Farèse extension of Brans-Dicke theory. We use the Bondi-Sachs framework to compute the field equations in Bondi-Sachs form, the asymptotically flat solutions, and the leading gravitational-wave memory effects. Although Damour-Esposito-Farèse theory has additional nonlinearities not present in Brans-Dicke theory, these nonlinearities are subleading effects; thus, the two theories share many similarities in the leading (and some subleading) solutions to hypersurface equations, asymptotic symmetries, and types of memory effects. The conservation equations for the mass and angular momentum aspects differ between the two theories, primarily because of the differences in the evolution equation for the scalar field. This leads to differences in the time dependence of the gravitational-wave memory signals that are produced during the quasicircular inspiral of compact binaries. These differences, however, are of second-order in a small coupling parameter of these theories, which suggests that it would be challenging to use memory effects to distinguish between these two theories. Nevertheless, our results can be used to analyze and interpret memory effects from numerical-relativity simulations of binaries in this theory.
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