Gravitational backreaction on a cosmic string: Formalism
Gravitational backreaction on a cosmic string: Formalism
复制标题
DOI：
10.1103/physrevd.99.084036
复制
发表时间：
2018-08
影响因子：
5
通讯作者：
D. Chernoff;'. Flanagan;B. Wardell
中科院分区：
文献类型：
--
作者：
D. Chernoff;'. Flanagan;B. Wardell
我们开发了一种方法来计算线性化的引力反作用的南部-后藤字符串使用一个完全协变的形式主义。我们的工作与运动方程表示在一个更高的维度模拟的测地线方程自我生成的强迫条款。该方法允许任意时空和世界片规范的背景和扰动的选择。扰动的时空度规可以表示为在弦世界片上支持的分布应力-能量张量上的积分。通过形式上对分布求积分，这个量可以重新表示为对弦的延迟像的积分。在这样做的时候，我们必须特别注意场点和弦的非光滑区域的贡献。然后，扰动度规的梯度分解为边界项和体项之和。分解取决于用来描述字符串的世界表坐标，但总和与这些考虑无关。我们用数值计算的方法说明了在世界表上的每一个点的自作用力的扭结，尖点和自相交使用各种不同的坐标选择的循环。对于世界片光滑部分上的场点，自作用力是有限的。当场点接近扭结或尖点时，自作用力发散，但在世界片的位移保持有限的意义上是可积的。作为一致性检查，我们验证了在无穷远的能量动量的周期平均通量匹配的直接工作的自我力执行的字符串。该方法可用于解决弦环演化的许多基本问题。
We develop a method for computing the linearized gravitational backreaction for Nambu-Goto strings using a fully covariant formalism. We work with equations of motion expressed in terms of a higher dimensional analog of the geodesic equation subject to self-generated forcing terms. The approach allows arbitrary spacetime and world sheet gauge choices for the background and perturbation. The perturbed spacetime metric may be expressed as an integral over a distributional stress-energy tensor supported on the string world sheet. By formally integrating out the distribution, this quantity may be reexpressed in terms of an integral over the retarded image of the string. In doing so, one must pay particular attention to contributions that arise from the field point and from nonsmooth regions of the string. Then, the gradient of the perturbed metric decomposes into a sum of boundary and bulk terms. The decomposition depends upon the world sheet coordinates used to describe the string, but the total is independent of those considerations. We illustrate the method with numerical calculations of the self-force at every point on the world sheet for loops with kinks, cusps and self-intersections using a variety of different coordinate choices. For field points on smooth parts of the world sheet the self-force is finite. As the field point approaches a kink or cusp the self-force diverges, but is integrable in the sense that the displacement of the world sheet remains finite. As a consistency check, we verify that the period-averaged flux of energy-momentum at infinity matches the direct work the self-force performs on the string. The methodology can be applied to address many fundamental questions for string loop evolution.