Growing hair on the extremal BTZ black hole. (English) Zbl 1370.83052
Summary: We show that the nonlinear \(\sigma\)-model in an asymptotically \(\mathrm{AdS}_3\) spacetime admits a novel local symmetry. The field action is assumed to be quartic in the nonlinear \(\sigma\)-model fields and minimally coupled to gravity. The local symmetry transformation simultaneously twists the nonlinear \(\sigma\)-model fields and changes the spacetime metric, and it can be used to map the extremal BTZ black hole to infinitely many hairy black hole solutions.
MSC:
| 83C57 | Black holes |
| 83C20 | Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory |
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