Nonlinear dynamics in the Einstein-Gauss-Bonnet gravity

Abstract

We numerically investigated how the 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 (αGB). We also observed that a collision of large scalar pulses will produce a large-curvature region, of which the magnitude also depends on αGB. For both models, the normal corrections (αGB > 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.

Autonomous Dynamical System of Einstein-Gauss-Bonnet Cosmologies

“…Similar results concerning the linear and non-linear dynamics of the theory, for either astrophysical or cosmological solutions can be found in the literature, for example see Ref. [34,35] for a numerical approach and Ref. [20,21] for an analytical approach.…”

Quasinormal modes, scattering, and Hawking radiation in the vicinity of an Einstein-dilaton-Gauss-Bonnet black hole

“…Let us notice that the Gauss-Bonnet term at some critical value of p might also produce the socalled eikonal instability (see, for example, [30,31,33,34] and references therein), which occurs at high multipole numbers ℓ and which was not analyzed for the case of the EdGB black hole in the literature so far. Recent studies of instabilities of wormhole solutions in the EdGB theory show agreement between the linear [35] and nonlinear [36] perturbations and come to the same conclusion on the instability of wormholes at whatever small value of the coupling constant.…”

No stable wormholes in Einstein-dilaton-Gauss-Bonnet theory

“…The spherically symmetric wormholes in the Gauss-Bonnet theory allow for the consistent dual-null formulation of the initial conditions for the nonlinear dynamics for massless matter. In particular, it was recently shown in [47] that the fate of a perturbed spherically symmetric wormhole supported by scalar fields is either a black hole or an expanding throat depending on the total energy of the structure. This result supports our general conclusion that the Kanti-Kleihaus-Kunz wormholes are unstable.…”