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

Abstract

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.

Gravitational collapse involving electric charge in the decoupling limit of the dilatonic Gauss--Bonnet gravity

“…As values of the model parameters increase, the black holes form later in terms of retarded time and both their radii and masses become smaller, up to an extremum, in which the tendencies reverse. Similar dependencies were observed in the case of non-minimal scalar-gravity couplings during dynamics investigations within the theory involving Higgs and dark matter sectors [27]. The only difference between the dependencies on the model parameters is that the changes are more significant for small values of α and large values of γ.…”

“…The analysed quantities were energy density ρ, radial pressure pr and pressure anisotropy pa ≡ pt − pr . Their precise covariant derivation for any general case can be found in [27]. Moreover, local temperature T l = κ l 2π with the surface gravity defined as κ l = a ,u a −2 [46,47] was also calculated.…”