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重力波非线性相互作用中匹配关系的数值研究

, PP. 798-809

Keywords: 重力波,非线性相互作用,匹配条件,失配度

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Abstract:

?应用一个二阶时空精度的非线性数值模式,模拟了重力波的非线性相互作用过程,讨论了重力波在相互作用中波长和频率的匹配关系.在共振相互作用中,三波的波长和频率都满足共振匹配条件.由于相互作用波遵从共振条件,共振相互作用显示出可逆的激发特征,即对一个共振波组,任意选取其中两支波作为初始波扰动,通过和或差的共振相互作用,能够激发出第三支波.对于非共振相互作用,数值结果表明,在相互作用中,波矢量在单一方向,通常是水平方向,趋近于匹配.三波的频率可能趋近于匹配,具体的失配程度可能取决于波数和频率失配的联合效应,也就是说,总的失配效果要有利于最大限度的能量交换.重力波在非共振相互作用中的这种匹配和失配关系不同于弱相互作用理论的结果.在弱相互作用理论中,波矢量应该满足共振匹配条件,波频率可以出现失配,而且生成波和次波的频率会发生振荡,振动幅度为频率失配值的一半.与共振相互作用不同,非共振相互作用展示出不可逆的激发特征.由于复杂性,难以确定非共振相互作用中波数和频率的失配程度,因此,对于指定的初始主次波,还不能完全预言出生成波的波数和频率的大小.

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