In AdS3, a relaxed class of boundary conditions makes Einstein's equations reduce to two AKNS integrable hierarchies, and stationary black holes in this class have constant temperatures fixed by hyperelliptic spectra, illustrated by a cnoidal KdV black hole.
B\"acklund transformations in 2D dilaton gravity
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abstract
We give a B\"acklund transformation connecting a generic 2D dilaton gravity theory to a generally covariant free field theory. This transformation provides an explicit canonical transformation relating both theories.
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Integrable black hole dynamics in the asymptotic structure of AdS$_{3}$
In AdS3, a relaxed class of boundary conditions makes Einstein's equations reduce to two AKNS integrable hierarchies, and stationary black holes in this class have constant temperatures fixed by hyperelliptic spectra, illustrated by a cnoidal KdV black hole.