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Sparse Spectral-Element Methods for the Helically Reduced Einstein Equations

机译:螺旋约化爱因斯坦方程的稀疏谱元方法

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To model the inspiral and merger of binary objects (blackholes or neutron stars), many researchers have been solving the Einstein equations numerically. Such simulation involves both the construction of gravitational initial data at time t_0 and its subsequent evolution to a final time t_F(») t_0. Interpretation of experimental detections of gravitational waves relies on numerical simulation. Moreover, detection of weak signals is facilitated by statistical techniques alongside "template banks" of numerically generated signals. We consider a nonstandard problem, solution of the Einstein equations reduced by helical symmetry, as described by Beetle, Bromley, Hernandez, and Price (BBHP) [1,2]. Heuristically, helical reduction is a data+evolution synthesis. Although solutions to the BBHP equations are ultimately unphysical, they may approximate the early phase of inspiral and serve as reduced order models.
机译:为了模拟二元物体(黑洞或中子星)的激发和合并,许多研究人员一直在数值上求解爱因斯坦方程。这种模拟既涉及在时间t_0上的引力初始数据的构造,又包括其到最终时间t_F(»)t_0的后续演变。引力波实验检测的解释依赖于数值模拟。此外,通过统计技术以及数字生成信号的“模板库”,可以促进对弱信号的检测。我们考虑了一个非标准问题,即通过螺旋对称减少的爱因斯坦方程组的解,如Beetle,Bromley,Hernandez和Price(BBHP)所述[1,2]。试探性地,螺旋减少是一种数据+进化综合。尽管BBHP方程的解决方案最终是非物理的,但它们可能接近吸气的早期阶段,并可用作降阶模型。

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