We numerically investigated how nonlinear dynamics depends on the dimensionality and on the higher-order curvature corrections in the form of Gauss-Bonnet (GB) terms. We especially monitored the processes of appearances of a singularity (or black hole) in two models: (i) a perturbed wormhole throat in spherically symmetric space-time, and (ii) colliding scalar pulses in plane-symmetric space-time. We used a dual-null formulation for evolving the field equations, which enables us to locate the trapping horizons directly, and also enables us to follow close to the large-curvature region due to its causal integrating scheme. We observed that the fate of a perturbed wormhole is either a black hole or an expanding throat depending on the total energy of the structure, and its threshold depends on the coupling constant of the GB terms (${\alpha }_{\mathrm{GB}}$). We also observed that a collision of large scalar pulses will produce a large-curvature region, of which the magnitude also depends on ${\alpha }_{\mathrm{GB}}$. For both models, the normal corrections (${\alpha }_{\mathrm{GB}}>0$) work for avoiding the appearance of singularity, although it is inevitable. We also found that in the critical situation for forming a black hole, the existence of the trapped region in the Einstein-GB gravity does not directly indicate the formation of a black hole.

• Received 7 June 2017

DOI:https://doi.org/10.1103/PhysRevD.96.044009