  Recent studies of nearby globular clusters have discovered excess dark mass
in their cores, apparently in an extended distribution, and simulations
indicate that this mass is composed mostly of white dwarfs (respectively
stellar-mass black holes) in clusters that are core-collapsed (respectively
with a flatter core). We perform mass-anisotropy modelling of the closest
globular cluster, M4, with intermediate slope for the inner stellar density. We
use proper-motion data from Gaia EDR3 and from observations by the Hubble Space
Telescope. We extract the mass profile employing Bayesian Jeans modelling, and
check our fits with realistic mock data. Our analyses return isotropic motions
in the cluster core and tangential motions ($\beta\approx -0.4$$\pm$$0.1$) in
the outskirts. We also robustly measure a dark central mass of roughly
$800\pm300 \,$M$_{\odot}$, but it is not possible to distinguish between a
point-like source, such as an intermediate-mass black hole (IMBH), or a dark
population of stellar remnants of extent $\approx 0.016\,\rm pc \simeq
3300\,AU$. However, when removing a high-velocity star from the cluster centre,
the same mass excess is found, but more extended ($\sim 0.034\, \rm{pc} \approx
7000\,\rm AU$). We use Monte Carlo $N$-body models of M4 to interpret the
second outcome, and find that our excess mass is not sufficiently extended to
be confidently associated with a dark population of remnants. Finally, we
discuss the feasibility of these two scenarios (i.e., IMBH vs. remnants), and
propose new observations that could help to better grasp the complex dynamics
in M4's core.
