The near-horizon region of rapidly spinning astrophysical black holes possess an AdS-like throat geometry and the associated conformal symmetry. In this talk wWe discuss implications of this symmetry for extracting physical properties of high-spin black holes from electromagnetic emissions in their near-vicinity. Specifically, we first use the emergent near-horizon conformal symmetry to find analytically near-superradiant null geodesics which extend from the near-horizon region out to a distant observatory. We then compute the broadening of electromagnetic line emissions from the innermost part of an accreting disk and find that the result is independent of the disk’s surface emissivity and therefore universal. This is an example of critical behavior in astronomy that is potentially observable by current or future telescopes.