The first stars are believed to have formed a few hundred million years after the big bang in so-called dark matter minihalos with masses $\sim 10^{6}\mbox{ M}_{\odot}$ . Their radiation lit up the Universe for the first time, and the supernova explosions that ended their brief lives enriched the intergalactic medium with the first heavy elements. Influenced by their feedback, the first galaxies assembled in halos with masses $\sim10^{8}\mbox{ M}_{\odot}$ , and hosted the first metal-enriched stellar populations. In this review, I summarize the theoretical progress made in the field of high-redshift star and galaxy formation since the turn of the millennium, with an emphasis on numerical simulations. These have become the method of choice to understand the multi-scale, multi-physics problem posed by structure formation in the early Universe. In the first part of the review, I focus on the formation of the first stars in minihalos - in particular the post-collapse phase, where disk fragmentation, protostellar evolution, and radiative feedback become important. I also discuss the influence of additional physical processes, such as magnetic fields and streaming velocities. In the second part of the review, I summarize the various feedback mechanisms exerted by the first stars, followed by a discussion of the first galaxies and the various physical processes that operate in them.

中文翻译：

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高红移宇宙的数值边界

据信，第一批恒星形成于质量为$ \ sim 10 ^ {6} \ mbox {M} _ {\ odot} $的所谓暗物质迷你晕大爆炸之后的几亿年。他们的辐射首次照亮了宇宙，结束了短暂生命的超新星爆炸使星际中间的介质富含了第一批重元素。受它们的反馈影响，第一批星系聚集在质量为\\ sim10 ^ {8} \ mbox {M} _ {\ odot} $的光环中，并容纳了首批富含金属的恒星族。在这篇综述中，我总结了自千年之交以来高红移星和星系形成领域的理论进展，重点是数值模拟。这些已成为了解早期宇宙中结构形成所带来的多尺度，多物理问题的一种选择方法。在审查的第一部分中，我重点介绍了微型晕圈中第一批恒星的形成-尤其是崩溃后阶段，在该阶段，磁盘碎片，原恒星演化和辐射反馈变得很重要。我还将讨论其他物理过程的影响，例如磁场和流速度。在本文的第二部分中，我总结了第一批恒星施加的各种反馈机制，然后讨论了第一批星系以及在其中运行的各种物理过程。例如磁场和流速度。在本文的第二部分中，我总结了第一批恒星施加的各种反馈机制，然后讨论了第一批星系以及在其中运行的各种物理过程。例如磁场和流速度。在本文的第二部分中，我总结了第一批恒星施加的各种反馈机制，然后讨论了第一批星系以及在其中运行的各种物理过程。