Horndeski引力中的非线性引力波：标量脉冲与记忆效应
Nonlinear gravitational waves in Horndeski gravity: Scalar pulse and memories
AI总结：
本文提出Horndeski引力中由标量单极子经形变映射生成的非微扰辐射解，证明非线性标量-张量混合可产生剪切，并分析脉冲后的记忆效应。
摘要：
我们提出并分析了一个新的Horndeski引力的非微扰辐射解。该精确解通过对平移对称爱因斯坦-标量系统中属于Robinson-Trautman几何的种子解进行形变映射构建，该种子解描述了由时变标量单极子发射的引力辐射。在详细分析种子解的性质后，我们表明：虽然广义相对论解允许无剪切的平行输运零标架，但形变解只能允许具有非零剪切的平行输运零标架。这一结果表明，在非线性层面，源自Horndeski动力学中高阶项的标量-张量混合可以从纯标量单极子产生剪切。我们进一步通过识别形变解中的自旋-0和自旋-2极化来确认这一分析，使用了我们辐射解的Penrose极限。最后，我们计算了在脉冲通过后，具有零初始相对速度的两个零测试粒子的测地线运动和记忆效应。这一精确辐射解为在高阶标量-张量理论中观察标量-张量混合的非线性后果提供了一个简单框架。
英文摘要：
We present and analyze a new non-perturbative radiative solution of Horndeski gravity. This exact solution is constructed by a disformal mapping of a seed solution of the shift-symmetric Einstein-Scalar system belonging to the Robinson-Trautman geometry describing the gravitational radiation emitted by a time-dependent scalar monopole. After analyzing in detail the properties of the seed, we show that while the general relativity solution allows for shear-free parallel transported null frames, the disformed solution can only admit parallel transported null frames with a non-vanishing shear. This result shows that, at the nonlinear level, the scalar-tensor mixing descending from the higher-order terms in Horndeski dynamics can generate shear out of a pure scalar monopole. We further confirm this analysis by identifying the spin-0 and spin-2 polarizations in the disformed solution using the Penrose limit of our radiative solution. Finally, we compute the geodesic motion and the memory effects experienced by two null test particles with vanishing initial relative velocity after the passage of the pulse. This exact radiative solution offers a simple framework to witness nonlinear consequences of the scalar-tensor mixing in higher-order scalar-tensor theories.
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