Understanding critical collapse of a scalar field
Gundlach, Carsten (1997) Understanding critical collapse of a scalar field Physical Review D, 55, (2), pp. 73537360. (doi:10.1103/PhysRevD.55.695).
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Description/Abstract
I construct a spherically symmetric solution for a massless real scalar field minimally coupled to general relativity which is discretely selfsimilar (DSS) and regular. This solution coincides with the intermediate attractor found by Choptuik in critical gravitational collapse. The echoing period is ?=3.4453±0.0005. The solution is continued to the future selfsimilarity horizon, which is also the future light cone of a naked singularity. The scalar field and metric are C1 but not C2 at this Cauchy horizon. The curvature is finite nevertheless, and the horizon carries regular null data. These are very nearly flat. The solution has exactly one growing perturbation mode, thus confirming the standard explanation for universality. The growth of this mode corresponds to a critical exponent of ?=0.374±0.001, in agreement with the best experimental value. I predict that in critical collapse dominated by a DSS critical solution, the scaling of the black hole mass shows a periodic wiggle, which like ? is universal. My results carry over to the free complex scalar field. Connections with previous investigations of selfsimilar scalar field solutions are discussed, as well as an interpretation of ? and ? as anomalous dimensions.
Item Type:  Article  

Digital Object Identifier (DOI):  doi:10.1103/PhysRevD.55.695  
ISSNs:  15507998 (print) 

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ePrint ID:  29173  
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Date Deposited:  07 Feb 2007  
Last Modified:  16 Apr 2017 22:23  
Further Information:  Google Scholar  
URI:  http://eprints.soton.ac.uk/id/eprint/29173 
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