  We reduce the BTZ spacetime to two kinds of hypersurfaces of foliation: one
having a fixed radial coordinate and the other a fixed angular coordinate. The
radial reduction leads to a Liouville type theory, and confirms, from the first
principle, the expectation laid out in the literature. In the other endeavor,
the angular reduction of the 3D gravity is carried out in two different ways;
the first again yields a Liouville type theory (different from that of the
radial reduction) and the second yields a 2D interacting quantum field theory
with quartic potential. Finally we discuss potential implications of our result
for the Equivalence Principle and Purity of Hawking radiation.
