引力坍缩标量场背景下测地线汇的演化
Evolution of geodesic congruences in a gravitationally collapsing scalar field background
摘要：
研究了球对称、非静态、非均匀时空中类时测地同余的演化，它代表了无质量标量场的引力坍缩。我们描绘了如何初始值的膨胀，旋转和剪切的一个同余，以及时空曲率，影响的全球行为和聚焦性能的一个家庭的轨迹。在特定的条件下，膨胀标量显示出有限的跳跃（从负值到正值）聚焦之前，最终发生。这种非单调的行为的扩展，在我们的数值工作中观察到的，成功地解释了通过分析方程的扩展。最后，我们提出的作用的度量参数（有关非静态和空间不均匀性），在塑造整体行为的测地同余。
英文摘要：
The evolution of timelike geodesic congruences in a spherically symmetric, nonstatic, inhomogeneous spacetime representing gravitational collapse of a massless scalar field is studied. We delineate how initial values of the expansion, rotation and shear of a congruence, as well as the spacetime curvature, influence the global behavior and focusing properties of a family of trajectories. Under specific conditions, the expansion scalar is shown to exhibit a finite jump (from negative to positive value) before focusing eventually occurs. This nonmonotonic behavior of the expansion, observed in our numerical work, is successfully explained through an analysis of the equation for the expansion. Finally, we bring out the role of the metric parameters (related to nonstaticity and spatial inhomogeneity), in shaping the overall behavior of geodesic congruences.
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