We proceed to study a (1+1)-dimensional dilaton gravity system with a
hyperbolic dilaton potential. Introducing a couple of new variables leads to
two copies of Liouville equations with two constraint conditions. In
particular, in conformal gauge, the constraints can be expressed with
Schwarzian derivatives. We revisit the vacuum solutions in light of the new
variables and reveal its dipole-like structure. Then we present a
time-dependent solution which describes formation of a black hole with a pulse.
Finally, the black hole thermodynamics is considered by taking account of
conformal matters from two points of view: 1) the Bekenstein-Hawking entropy
and 2) the boundary stress tensor. The former result agrees with the latter one
with a certain counter-term.Comment: 23 page
