Gravitational dynamics in the toy model of the Higgs-dark matter sector: the field theoretic perspective

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–Nordström 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–Nordström spacetimes. The apparent horizon local temperature changes monotonically in the minimally coupled case and non-monotonically when non-minimal scalar–gravity couplings are involved