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Abstract

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.