On the existence of self-similar spherically symmetric wave maps coupled to gravity

Details On the existence of self-similar spherically symmetric wave maps coupled to gravity On the existence of self-similar spherically symmetric wave maps coupled to gravity

2002-01-14

arxiv.org/abs/gr-qc/0201046v1

Class.Quant.Grav.19:3309-3322,2002

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, LaTex

Scientific paper

10.1088/0264-9381/19/12/313

We present a detailed analytical study of spherically symmetric self-similar solutions in the SU(2) sigma model coupled to gravity. Using a shooting argument we prove that there is a countable family of solutions which are analytic inside the past self-similarity horizon. In addition, we show that for sufficiently small values of the coupling constant these solutions possess a regular future self-similarity horizon and thus are examples of naked singularities. One of the solutions constructed here has been recently found as the critical solution at the threshold of black hole formation.

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