  The study of 2-dimensional surfaces of constant curvature constitutes a
beautiful branch of geometry with well-documented ties to the mathematical
physics of integrable systems. A lesser known, but equally fascinating, fact is
its connection to 2-dimensional gravity; specifically Jackiw-Teitelboim (JT)
gravity, where the connection manifests through a coordinate choice that
roughly speaking re-casts the gravitational field equations as the sine-Gordon
equation. In this language many well-known results, such as the JT-gravity
black hole and its properties, were understood in terms of sine-Gordon solitons
and their properties. In this brief note, we revisit these ideas in the context
of some of the recent exciting developments in JT-gravity and, more generally,
low-dimensional quantum gravity and speculate on how some of these new ideas
may be similarly understood.
