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arXiv 1607.04202gr-qcastro-ph.COastro-ph.HE
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引力波理论

Theory of Gravitational Waves

Alexandre Le Tiec, Jérôme Novak

摘要:

引力辐射的存在是对引力相互作用的任何相对论性描述的自然预言。在这一章中,我们将集中讨论爱因斯坦广义相对论所预言的引力波。首先,我们介绍那些数学概念,这些概念是必要的,以正确制定的物理理论,如流形,向量,张量,度量,连接和曲率的概念。其次,我们激励,制定,然后讨论爱因斯坦的方程,它涉及到时空的几何形状,其物质含量。引力波后来被引入作为平坦时空周围的线性化爱因斯坦方程的解。这些波以光速传播,并具有两个偏振态。引力波可以与物质相互作用,从而可以通过激光干涉仪直接检测。最后,我们导出了爱因斯坦四极公式,并用来说明以相对论速度运动的非球形致密天体是强有力的引力波源。

英文摘要:

The existence of gravitational radiation is a natural prediction of any relativistic description of the gravitational interaction. In this chapter, we focus on gravitational waves, as predicted by Einstein's general theory of relativity. First, we introduce those mathematical concepts that are necessary to properly formulate the physical theory, such as the notions of manifold, vector, tensor, metric, connection and curvature. Second, we motivate, formulate and then discuss Einstein's equation, which relates the geometry of spacetime to its matter content. Gravitational waves are later introduced as solutions of the linearized Einstein equation around flat spacetime. These waves are shown to propagate at the speed of light and to possess two polarization states. Gravitational waves can interact with matter, allowing for their direct detection by means of laser interferometers. Finally, Einstein's quadrupole formulas are derived and used to show that nonspherical compact objects moving at relativistic speeds are powerful gravitational wave sources.

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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