Critical collapse of the massless scalar field in axisymmetry

Abstract

We present the results from a numerical study of critical gravitational collapse of axisymmetric distributions of massless scalar field energy. We find threshold behavior that can be described by the spherically symmetric critical solution with axisymmetric perturbations. However, we see indications of a growing, nonspherical mode about the spherically symmetric critical solution. The effect of this instability is that the small asymmetry present in what would otherwise be a spherically symmetric self-similar solution grows. This growth continues until a bifurcation occurs and two distinct regions form on the axis, each resembling the spherically symmetric self-similar solution. The existence of a nonspherical unstable mode is in conflict with previous perturbative results, and we therefore discuss whether such a mode exists in the continuum limit, or whether we are instead seeing a marginally stable mode that is rendered unstable by numerical approximation.

Choptuik’s scaling in higher dimensions

“…We believe that an improved code will discover that the behavior close to the pinching is similar to what happens in the axisymmetric near-critical collapse. In the latter case, evidence was given in [25] that a non-spherical mode appears causing 10 The critical dimensions in this system are: (i) Dmerger = 10, above which the local geometry near the merger point argued to be cone-like, and below which this cone-like behavior is spontaneously broken [5,21], and (ii) D (2d order) = 13 above which the phase transition becomes of second order [6,7]. 11 We note, however, that it is still not quite clear how to relate the Choptuik solution emerging in the collapse situation to its time-symmetric version studied in [14].…”

Critical phenomena in the aspherical gravitational collapse of radiation fluids

“…In general these codes can be run with different slicing and gauge conditions, but the "1+log" and "Gammadriver" conditions (see eqs. (8) and (9) below) have proven particularly useful for simulations of spacetimes containing black holes. How suitable these codes are for simulations of critical collapse, however, remains a somewhat open question (see also [10,23,24] for recent discussions.)…”

Exploring an S-matrix for gravitational collapse II: a momentum space analysis

“…The results can then be compared with those coming from closed trapped surface (CTS) criteria [7,8] and will be tested, hopefully in the near future, against numerical GR calculations (see [9,10] for a few results already available for this case).…”