We present a novel approach to compute systematically the relativistic projection effects at any order in perturbation theory within the weak field approximation. In this derivation the galaxy number counts is written completely in terms of the redshift perturbation. The relativistic effects break the symmetry along the line-of-sight and they source, contrarily to the standard perturbation theory, the odd multipoles of the matter power spectrum or 2-point correlation function, providing a unique signature for their detection in Large Scale Structure surveys. We show that our approach agrees with previous derivations (up to third order) of relativistic effects and, for the first time, we derive a model for the transverse Doppler effect. Moreover, we proof that in the Newtonian limit this approach is consistent with standard perturbation theory at any order.

中文翻译：

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弱场近似中的相对论星系数

我们提出了一种新方法来系统地计算弱场近似内微扰理论中任何阶的相对论投影效应。在这个推导中，星系数量的计数完全是根据红移扰动来写的。相对论效应打破了视线的对称性，与标准微扰理论相反，它们产生了物质功率谱的奇多极或 2 点相关函数，为它们在大规模结构中的检测提供了独特的特征调查。我们表明我们的方法与先前的相对论效应推导一致（高达三阶），并且我们第一次推导出横向多普勒效应的模型。而且，