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

TL;DR

This paper investigates gravitational evolution and black hole formation in a toy model combining Higgs and dark matter sectors with non-minimal couplings to gravity, revealing how these interactions influence spacetime structures and horizon properties.

Contribution

It introduces a detailed analysis of gravitational dynamics in a Higgs-dark matter model with non-minimal couplings, highlighting the effects on black hole formation and horizon features.

Findings

Black hole structures are either Schwarzschild or Reissner-Nordström types.

Black hole formation timing and sizes depend on scalar mass parameters.

Non-minimal couplings cause non-monotonic changes in horizon temperature.

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-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.