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arXiv 2402.02497gr-qcastro-ph.CO
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约化Horndeski理论中的引力波能量动量张量

Gravitational wave energy momentum-tensor in reduced Horndeski theories

João C. Lobato, Maurício O. Calvão

AI总结:

该研究将Isaacson公式推广至约化Horndeski理论,推导引力波能量动量张量,并发现其迹在光速传播时为零,且非共形不变,部分子类散度不为零。

摘要:

我们仅在主导阶施加场方程,将Isaacson公式推广到Horndeski理论中张量模式以光速传播且存在标量波的一类(约化Horndeski理论),从而得到引力波能量动量张量(EMT)。我们讨论了重要的特殊情况,例如:标量波也以光速传播的理论,以及可以在任意开集中实现横向无迹规范的理论。对于所有波扰动都以光速传播的理论,引力波能量动量张量的迹为零。在其他情况下,迹被证明不平凡地不为零。作为我们一般结果的一个特例,我们在Brans-Dicke理论中获得了引力波EMT,既在爱因斯坦框架中(恢复了文献中的先前结果),也在Jordan框架中,从而表明引力波EMT不是共形不变的。我们进一步证明,在约化Horndeski理论的一个子类中,与广义相对论相反,即使在施加完整运动方程之后,引力波EMT的散度也不为零,假设采用eikonal解。

英文摘要:

We generalize, imposing the field equations only at dominant order, the Isaacson formula for the gravitational wave (GW) energy-momentum tensor (EMT) to the class of Horndeski theories in which the tensor modes travel at the speed of light (reduced Horndeski theories) and scalar waves are present. We discuss important particular cases such as: theories where scalar waves are also luminal and theories in which the transverse-traceless gauge can be achieved in an arbitrary open set. The vanishing of the trace of the gravitational wave energy-momentum tensor is obtained for theories in which all wave perturbations propagate at the speed of light. The trace is shown not to vanish trivially in other cases. We obtain, as a particular case of our general result, the GW EMTs, in a Brans-Dicke theory, both in the Einstein frame, recovering previous results in the literature, and in the Jordan frame, thereby showing the GW EMT is not conformally invariant. We further prove that there exists a subclass of reduced Horndeski theories where, in contrast to general relativity, the divergence of the GW EMT does not vanish even after the imposition of the full equations of motion, assuming an eikonal solution.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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