标题： 该类宇宙弦环的引力辐射的解析结果 显示英文标题

标题： Analytic Results for the Gravitational Radiation from a Class of Cosmic String Loops

摘要： 宇宙弦环由一对周期函数${\bf a}$和${\bf b}$定义，它们在三维空间中描绘出单位长度的闭合曲线。我们考虑一类特殊的环，其中${\bf a}$沿着一条直线，而${\bf b}$位于与该直线正交的平面上。对于这类宇宙弦环，可以给出引力波辐射功率$\gamma$的简单解析表达式。 我们精确地以闭合形式计算$\gamma$在几个特殊情况下：(1)${\bf b}$一个被遍历$M$次的圆；(2)${\bf b}$一个有$N$条边和内部顶点角$\pi-2\pi M/N$的正多边形；(3)${\bf b}$一个半角为$\theta$的等腰三角形。 我们证明在我们的特殊环类中，情况(1)中的$M=1$是$\gamma$的绝对最小值，并确定该类中$\gamma$的所有驻点。 显示英文摘要

摘要： Cosmic string loops are defined by a pair of periodic functions ${\bf a}$ and ${\bf b}$, which trace out unit-length closed curves in three-dimensional space. We consider a particular class of loops, for which ${\bf a}$ lies along a line and ${\bf b}$ lies in the plane orthogonal to that line. For this class of cosmic string loops one may give a simple analytic expression for the power $\gamma$ radiated in gravitational waves. We evaluate $\gamma$ exactly in closed form for several special cases: (1) ${\bf b}$ a circle traversed $M$ times; (2) ${\bf b}$ a regular polygon with $N$ sides and interior vertex angle $\pi-2\pi M/N$; (3) ${\bf b}$ an isosceles triangle with semi-angle $\theta$. We prove that case (1) with $M=1$ is the absolute minimum of $\gamma$ within our special class of loops, and identify all the stationary points of $\gamma$ in this class.