论文标题
麦克斯韦 - 斯卡尔场系统附近的空间无穷大
The Maxwell-scalar field system near spatial infinity
论文作者
论文摘要
我们利用弗里德里希（Friedrich）的空间无穷大的表示来研究麦克斯韦 - 斯卡尔场系统在空间无穷大的附近的渐近扩展。该分析的主要目的是了解该系统的非线性对解决方案的规律性和零无限范围的多均匀扩张的影响，尤其是在零无限触摸空间无穷大的关键集合中。我们分析的主要结果是，非线性相互作用使两个场在保形边界处的奇异性比无相互作用时所见。特别是，我们在渐近扩展中发现了一类全新的对数项，这取决于麦克斯韦和标量场之间的耦合常数。我们分析了这些结果对零无穷大的田地的剥离（或更确切地说是缺乏剥离）的含义。
We make use of Friedrich's representation of spatial infinity to study asymptotic expansions of the Maxwell-scalar field system near spatial infinity. The main objective of this analysis is to understand the effects of the non-linearities of this system on the regularity of solutions and polyhomogeneous expansions at null infinity and, in particular, at the critical sets where null infinity touches spatial infinity. The main outcome from our analysis is that the nonlinear interaction makes both fields more singular at the conformal boundary than what is seen when the fields are non-interacting. In particular, we find a whole new class of logarithmic terms in the asymptotic expansions which depend on the coupling constant between the Maxwell and scalar fields. We analyse the implications of these results on the peeling (or rather lack thereof) of the fields at null infinity.
