The relation between gravitational memory effects and Bondi-Metzner-Sachs symmetries of the asymptotically flat spacetimes is studied in the scalar-tensor theory. For this purpose, the solutions to the equations of motion near the future null infinity are obtained in the generalized Bondi-Sachs coordinates with a suitable determinant condition. It turns out that the Bondi-Metzner-Sachs group is also a semi-direct product of an infinite dimensional supertranslation group and the Lorentz group as in general relativity. There are also degenerate vacua in both the tensor and the scalar sectors in the scalar-tensor theory. The supertranslation relates the vacua in the tensor sector, while in the scalar sector, it is the Lorentz transformation that transforms the vacua to each other. So there are the tensor memory effects similar to the ones in general relativity, and the scalar memory effect, which is new. The evolution equations for the Bondi mass and angular momentum aspects suggest that the null energy fluxes and the angular momentum fluxes across the null infinity induce the transition among the vacua in the tensor and the scalar sectors, respectively.

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标量张量理论中的引力记忆效应和 Bondi-Metzner-Sachs 对称性

标量张量理论研究了引力记忆效应与渐近平坦时空的 Bondi-Metzner-Sachs 对称性之间的关系。为此，在具有合适行列式条件的广义 Bondi-Sachs 坐标中获得了接近未来零无穷大的运动方程的解。事实证明，邦迪-梅茨纳-萨克斯群也是广义相对论中无限维超平移群和洛伦兹群的半直积。在标量-张量理论中，在张量和标量扇区中也存在退化真空。超平移与张量扇区中的真空相关，而在标量扇区中，将真空相互转换的是洛伦兹变换。于是就有了类似于广义相对论中的张量记忆效应，以及新出现的标量记忆效应。邦迪质量和角动量方面的演化方程表明，零能量通量和角动量通量跨越零无穷大分别诱导张量和标量扇区中的真空之间的转变。