Shadows of Giants: Constraints on Stupendously Large Black Holes from Negative Sources against the Cosmic Microwave Background

Stupendously large astrophysical black holes (SLABs) are hypothetical black holes with masses of more than a trillion Suns. Because observable consequences of their existence have only recently been seriously considered, there have been relatively few constraints on their abundance. This work motivates a simple yet powerful constraint on SLABs: their huge shadows are visible against the cosmic microwave background. SLABs could thus appear as negative sources in microwave data. In fact, the shadow of a SLAB with a fixed mass becomes easier to detect with increasing redshifts past $1.6$ where the angular diameter distance starts falling. The limits are powerful enough to rule out SLABs of mass $\gtrsim {10}^{17}{M}_{\odot }$ within the last scattering surface, and imply ${\mathrm{\Omega }}_{BH}\lesssim {10}^{-5}$ for masses ${10}^{15}$–${10}^{18}{M}_{\odot }$. I also discuss the effects of accretion and their implications for the limits: SLAB growth, positive accretion luminosity, and obscuring material.