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

Abstract

The paper presents the course and outcomes of gravitational collapse of a selfinteracting electrically charged scalar field in the decoupling limit of the dilatonic Gauss-Bonnet gravity. The analyses were conducted with the use of double null coordinates, which allow to trace the evolutions within the whole spacetime, i.e., from approximately past null infinity up to the central hypersurface, which can be singular and surrounded by a horizon. The emerging spacetimes were either non-singular or, for sufficiently big scalar fields self-interaction strengths, singular and containing black holes of a Schwarzschild type. A size of the region, in which the gravitational dynamics was observed was controlled by an absolute value of the Gauss-Bonnet coupling. Dependencies of characteristics of the forming black holes on the dilatonic and Gauss-Bonnet parameters turned out to be similar in the case of black hole masses and radii as well as their time of formation in terms of retarded time. In the cases of masses and radii minima were observed, while in the remaining case a maximum existed. The electric charge of the emerging black holes possessed a maximum when measured versus the dilatonic coupling constant and was strictly decreasing with the Gauss-Bonnet coupling. All the characteristics changed monotonically with the field selfinteraction strengths. The times of formation and charges of black holes decreased, while masses and radii increased with the self-interaction strengths of the dynamical fields. Values of the energy density, radial pressure, pressure anisotropy and the collapsing scalar fields were the biggest along the null hypersurface of propagation of the initial peaks of the scalar fields. For big values of the Gauss-Bonnet coupling constant, an increase in their values was also observed in the vicinity of the central singularity within the whole range of advanced time. Non-zero values of the dilaton field outside the black hole event horizon may indicate a formation of a hairy black hole. The local temperature calculated along the apparent horizon was increasing for late times of the evolution, that is in non-dynamical spacetime regions, and exhibited extrema in areas, where the dynamics of the gravity-matter system was observed.