Unveiling Gargantua: A new search strategy for the most massive central
  cluster black holes
  We aim to unveil the most massive central cluster black holes in the
universe. We present a new search strategy which is based on a black hole mass
gain sensitive 'calorimeter' and which links the innermost stellar density
profile of a galaxy to the adiabatic growth of its central SMBH. In a first
step we convert observationally inferred feedback powers into SMBH growth rates
by using reasonable energy conversion efficiency parameters, $\epsilon$. In the
main part of this paper we use these black hole growth rates, sorted in
logarithmically increasing steps encompassing our whole parameter space, to
conduct $N$-Body computations of brightest cluster galaxies with the newly
developed MUESLI software. For the initial setup of galaxies we use core-Sersic
models in order to account for SMBH scouring. We find that adiabatically driven
core re-growth is significant at the highest accretion rates. As a result, the
most massive black holes should be located in BCGs with less pronounced cores
when compared to the predictions of empirical scaling relations which are
usually calibrated in less extreme environments. For efficiency parameters
$\epsilon<0.1$, BCGs in the most massive, relaxed and X-ray luminous galaxy
clusters might even develop steeply rising density cusps. Finally, we discuss
several promising candidates for follow up investigations, among them the
nuclear black hole in the Phoenix cluster. Based on our results, it might have
a mass of the order of $10^{11} M_\odot$.
