Black holes are unique among astrophysical sources: they are the simplest macroscopic objects in the Universe, and they are extraordinary in terms of their ability to convert energy into electromagnetic and gravitational radiation. Our capacity to probe their nature is limited by the sensitivity of our detectors. The LIGO/Virgo interferometers are the gravitational-wave equivalent of Galileo’s telescope. The first few detections represent the beginning of a long journey of exploration. At the current pace of technological progress, it is reasonable to expect that the gravitational-wave detectors available in the 2035-2050s will be formidable tools to explore these fascinating objects in the cosmos, and space-based detectors with peak sensitivities in the mHz band represent one class of such tools. These detectors have a staggering discovery potential, and they will address fundamental open questions in physics and astronomy. Are astrophysical black holes adequately described by general relativity? Do we have empirical evidence for event horizons? Can black holes provide a glimpse into quantum gravity, or reveal a classical breakdown of Einstein’s gravity? How and when did black holes form, and how do they grow? Are there new long-range interactions or fields in our Universe, potentially related to dark matter and dark energy or a more fundamental description of gravitation? Precision tests of black hole spacetimes with mHz-band gravitational-wave detectors will probe general relativity and fundamental physics in previously inaccessible regimes, and allow us to address some of these fundamental issues in our current understanding of nature.

黑洞在天体物理来源中是独一无二的：它们是宇宙中最简单的宏观物体，而且它们将能量转化为电磁和引力辐射的能力非凡。我们探测其本质的能力受到探测器灵敏度的限制。 LIGO/Virgo 干涉仪相当于伽利略望远镜的引力波。最初的几次探测代表着漫长探索之旅的开始。按照目前的技术进步速度，可以合理地预期 2035-2050 年代可用的引力波探测器将成为探索宇宙中这些迷人物体的强大工具，以及在 mHz 频段具有峰值灵敏度的天基探测器代表一类此类工具。这些探测器具有惊人的发现潜力，它们将解决物理学和天文学中的基本开放问题。广义相对论是否充分描述了天体物理黑洞？我们有事件视界的经验证据吗？黑洞能否让我们一睹量子引力，或者揭示爱因斯坦引力的经典崩溃？黑洞是如何、何时形成的，以及它们是如何生长的？我们的宇宙中是否存在新的远程相互作用或场，可能与暗物质和暗能量或更基本的引力描述有关？使用毫赫兹波段引力波探测器对黑洞时空进行精确测试将在以前无法达到的范围内探索广义相对论和基础物理学，并使我们能够解决当前对自然的理解中的一些基本问题。