The objective of the paper was to examine gravitational evolutions in the
Higgs--dark matter sector toy model. The real part of the Higgs doublet was
modelled by a neutral scalar. Two dark matter candidates introduced were the
dark photon and a charged complex scalar. Non-minimal couplings of both scalars
to gravity were included. The coupling channels between the ordinary and dark
matter sectors were kinetic mixing between the electromagnetic and dark U(1)
fields and the Higgs portal coupling among the scalars. The structures of
emerging singular spacetimes were either of Schwarzschild or
Reissner-Nordstr\"{o}m types. The non-minimal scalar--gravity couplings led to
an appearance of timelike portions of apparent horizons where they transform
from spacelike to null. The features of dynamical black holes were described as
functions of the model parameters. The black holes formed later and their radii
and masses were smaller as the mass parameter of the complex scalar increased.
The dependencies on the coupling of the Higgs field to gravity exhibited
extrema, which were a maximum for the time of the black holes formation and
minima in the cases of their radii and masses. A set of quantities associated
with an observer moving with the evolving matter was proposed. The energy
density, radial pressure and pressure anisotropy within dynamical spacetimes
get bigger as the singularity is approached. The increase is more considerable
in the Reissner-Nordstr\"{o}m spacetimes. The apparent horizon local
temperature changes monotonically in the minimally coupled case and
non-monotonically when non-minimal scalar--gravity couplings are involved.Comment: 38 pages, 21 figure
