M87* in space, time, and frequency
  Observing the dynamics of compact astrophysical objects provides insights
into their inner workings, thereby probing physics under extreme conditions.
The immediate vicinity of an active supermassive black hole with its event
horizon, photon ring, accretion disk, and relativistic jets is a perfect pace
to study general relativity, magneto-hydrodynamics, and high energy plasma
physics. The recent observations of the black hole shadow of M87* with Very
Long Baseline Interferometry (VLBI) by the Event Horizon Telescope (EHT) open
the possibility to investigate its dynamical processes on time scales of days.
In this regime, radio astronomical imaging algorithms are brought to their
limits. Compared to regular radio interferometers, VLBI networks typically have
fewer antennas and low signal to noise ratios (SNRs). If the source is variable
during the observational period, one cannot co-add data on the sky brightness
distribution from different time frames to increase the SNR. Here, we present
an imaging algorithm that copes with the data scarcity and the source's
temporal evolution, while simultaneously providing uncertainty quantification
on all results. Our algorithm views the imaging task as a Bayesian inference
problem of a time-varying brightness, exploits the correlation structure
between time frames, and reconstructs an entire, $\mathbf{2+1+1}$ dimensional
time-variable and spectrally resolved image at once. The degree of correlation
in the spatial and the temporal domains is inferred from the data and no form
of correlation is excluded a priori. We apply this method to the EHT
observation of M87* and validate our approach on synthetic data. The time- and
frequency-resolved reconstruction of M87* confirms variable structures on the
emission ring on a time scale of days. The reconstruction indicates extended
and time-variable emission structures outside the ring itself.
