论文标题
对非线性重力波性质的新见解
New Insights into the Nature of Nonlinear Gravitational Waves
论文作者
论文摘要
我们研究重力波的演化方程，这些方程是使用完整度量来提出和降低指标的。该方法确保了RICCI张量与所有量规限制和要求之间的完全一致性，并允许将所有张量的有意义扩展到二阶，从而避免了以前工作中观察到的几种不一致和矛盾。在扰动理论中将谐波量规延伸到二阶导致新的非线性方程。我们表明，该方程式的非平凡解是具有非零迹线的非平面波模式。这些解决方案必须包含纵向和横向组件，因为仪表限制都允许两者。
We study the evolution equations for gravitational waves, which are derived using the full metric to raise and lower indices. This method ensures full consistency between the Ricci tensor and all gauge restrictions and requirements, and allows a meaningful expansion of all tensors up to second order, avoiding several inconsistencies and contradictions observed in previous work. Taking the harmonic gauge to second order in the perturbation theory results in a new nonlinear equation. We show that non-trivial solutions to this equation are necessarily non-plane wave modes with a non-zero trace. These solutions must contain both longitudinal and transverse components, as both are permitted by the gauge restrictions.
