Analytic evidence for continuous self-similarity of the critical merger solution

Vadim Asnin*, Barak Kol, Michael Smolkin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


The double cone, a cone over a product of a pair of spheres, is known to play a role in the black-hole black-string phase diagram, and like all cones it is continuously self-similar (CSS). Its zero modes spectrum (in a certain sector) is determined in detail, and it implies that the double cone is a co-dimension 1 attractor in the space of those perturbations which are smooth at the tip. This is interpreted as strong evidence for the double cone being the critical merger solution. For the non-symmetry-breaking perturbations we proceed to perform a fully nonlinear analysis of the dynamical system. The scaling symmetry is used to reduce the dynamical system from a 3D phase space to 2D, and obtain the qualitative form of the phase space, including a non-perturbative confirmation of the existence of the 'smoothed cone'.

Original languageAmerican English
Article number013
JournalClassical and Quantum Gravity
Issue number23
StatePublished - 7 Dec 2006

Bibliographical note

Funding Information:
This research is supported in part by The Israel Science Foundation grant no 607/05 and by The Binational Science Foundation BSF-2004117.


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