  In 1977, Blandford and Znajek showed that the electromagnetic field
surrounding a rotating black hole can harvest its spin energy and use it to
power a collimated astrophysical jet, such as the one launched from the center
of the elliptical galaxy M87. Today, interferometric observations with the
Event Horizon Telescope (EHT) are delivering high-resolution,
event-horizon-scale, polarimetric images of the supermassive black hole M87* at
the jet launching point. These polarimetric images offer an unprecedented
window into the electromagnetic field structure around a black hole. In this
paper, we show that a simple polarimetric observable -- the phase
$\angle\beta_2$ of the second azimuthal Fourier mode of the linear polarization
in a near-horizon image -- depends on the sign of the electromagnetic energy
flux and therefore provides a direct probe of black hole energy extraction. In
Boyer-Lindquist coordinates, the Poynting flux for axisymmetric electromagnetic
fields is proportional to the product $B^\phi B^r$. The phase $\angle\beta_2$
likewise depends on the ratio $B^\phi/B^r$, thereby enabling an observer to
experimentally determine the direction of electromagnetic energy flow in the
near-horizon environment. Data from the 2017 EHT observations of M87* are
consistent with electromagnetic energy outflow. Currently envisioned
multi-frequency observations of M87* will achieve higher dynamic range and
angular resolution, and hence deliver measurements of $\angle\beta_2$ closer to
the event horizon as well as better constraints on Faraday rotation. Such
observations will enable a definitive test for energy extraction from the black
hole M87*.
