The cataclysmic observations of event GW170817, first as gravitational waves along the inspiral motion of two neutron stars, then as a short \(\gamma \)-ray burst, and later as a kilonova, launched the era of multimessenger astronomy, and played a pivotal role in furthering our understanding on a number of longstanding questions. Numerical modeling of such multimessenger sources is an important tool to understand the physics of compact objects and, more generally, the physics of matter under extreme conditions. In this review we present a unified view of various techniques used to obtain equilibrium and quasiequilibrium solutions for three astrophysically relevant relativistic, self-gravitating fluid systems: Binary neutron stars, black hole-disks, and magnetized rotating neutron stars. These solutions are necessary not only for modeling such compact objects, but equally important, for providing self-consistent initial data in numerical relativity simulations. Instead of presenting the full details of the formulations and numerical algorithms, we focus on painting the broadbrush picture of the methods developed to address these problems, and facilitate future work in the area.

对事件 GW170817 的灾难性观测，首先是沿着两颗中子星的吸气运动的引力波，然后是短的\(\gamma \)射线爆发，后来作为千新星，开启了多信使天文学的时代，并在加深我们对许多长期存在的问题的理解方面发挥了关键作用。这种多信使源的数值建模是理解致密物体物理的重要工具，更一般地说，是理解极端条件下物质物理的重要工具。在这篇综述中，我们对用于获得三种天体物理学相关的相对论、自引力流体系统的平衡和准平衡解的各种技术进行了统一的看法：双中子星、黑洞盘和磁化旋转中子星。这些解决方案不仅对于为此类紧凑对象建模是必要的，而且对于在数值相对论模拟中提供自洽的初始数据同样重要。