5.5 Critical collapse in semiclassical 5 Aspects of current research5.3 Analytic approaches

5.4 Astrophysical black holes

Any real world application of critical phenomena would require that critical phenomena are not an artifact of the simple matter models that have been studied so far, and that they are not an artifact of spherical symmetry. At present this seems a reasonable hypothesis.

Critical collapse still requires a kind of fine-tuning of initial data that does not seem to arise naturally in the astrophysical world. Niemeyer and Jedamzik [102] have suggested a scenario that gives rise to such fine-tuning. In the early universe, quantum fluctuations of the metric and matter can be important, for example providing the seeds of galaxy formation. If they are large enough, these fluctuations may even collapse immediately, giving rise to what is called primordial black holes. Large quantum fluctuations are exponentially more unlikely than small ones, tex2html_wrap_inline3463, where tex2html_wrap_inline3225 is the density contrast of the fluctuation. One would therefore expect the spectrum of primordial black holes to be sharply peaked at the minimal tex2html_wrap_inline3225 that leads to black hole formation. That is the required fine-tuning. In the presence of fine-tuning, the black hole mass is much smaller than the initial mass of the collapsing object, here the density fluctuation. In consequence, the peak of the primordial black hole spectrum might be expected to be at exponentially smaller values of the black hole mass than expected naively. See also [103, 124].

The primordial black holes work assumes that the critical phenomena will be of type II. If one could fine-tune the gravitational collapse of stars made of realistic matter (i.e. not scalar fields) it seems likely that type I critical phenomena could be observed, i.e. there would be a universal mass gap. Critical collapse is not likely to be relevant in the real universe (at least at the present epoch) as there is no mechanism for fine-tuning of initial data.

5.5 Critical collapse in semiclassical 5 Aspects of current research5.3 Analytic approaches

image Critical Phenomena in Gravitational Collapse
Carsten Gundlach
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