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arXiv 2006.13010gr-qc
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标量-张量理论中的类光激波

Light-like shockwaves in scalar-tensor theories

Bence Racskó, László Árpád Gergely

摘要:

电磁冲击波和引力波都以光速传播。如果它们携带大量的能量-动量,这将改变它们传播所经过的时空的性质。这可以用奇异的零超曲面所分隔的时空区域之间的连接条件来描述。我们推导了Brans-Dicke理论在Jordan框架中的通用连接条件,探索了一种基于横矢量而不是法线的形式主义,它可以应用于任何类型的超曲面。在非零超曲面的特殊情况下,我们得到一个广义Lanczos方程,其中的外在曲率的跳跃来源于分布能量动量张量和标量的横导数的跳跃。在零超曲面的情况下,分布源被分解为面密度、流和压力。然而,后者应该消失凭借标量结条件。

英文摘要:

Both electromagnetic shock-waves and gravitational waves propagate with the speed of light. If they carry significant energy-momentum, this will change the properties of the space-time they propagate through. This can be described in terms of the junction conditions between space-time regions separated by a singular, null hypersurface. We derived generic junction conditions for Brans-Dicke theory in the Jordan frame, exploring a formalism based on a transverse vector, rather than normal, which can be applied to any type of hypersurfaces. In the particular case of a non-null hypersurface we obtain a generalised Lanczos equation, in which the jump of the extrinsic curvature is sourced by both the distributional energy-momentum tensor and by the jump in the transverse derivative of the scalar. In the case of null hypersurfaces, the distributional source is decomposed into surface density, current and pressure. The latter however ought to vanish by virtue of the scalar junction condition.

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