The interplay between the diffeomorphism and conformal symmetries (a feature common in quantum field theories) is shown to be exhibited for the case of black holes in two dimensional classical Liouville theory. We show that although the theory is con
formally invariant in the near horizon limit, there is a breaking of the diffeomorphism symmetry at the classical level. On the other hand, in the region away from the horizon, the conformal symmetry of the theory gets broken with the diffeomorphism symmetry remaining intact.
Hawking radiation is obtained from the Reissner-Nordstr{o}m blackhole with a global monopole and the Garfinkle-Horowitz-Strominger blackhole falling in the class of the most general spherically symmetric blackholes $(sqrt{-g} eq1)$, using only chiral
anomaly near the event horizon and covariant boundary condition at the event horizon. The approach differs from the anomaly cancellation approach since apart from the covariant boundary condition, the chiral anomaly near the horizon is the only input to derive the Hawking flux.
We show that the diffeomorphism anomaly together with the trace anomaly reveal a chiral Virasoro algebra near the event horizon of a black hole. This algebra is the same irrespective of whether the anomaly is covariant or consistent, thereby manifest
ing its universal character and the fact that only the outgoing modes are relevant near the horizon. Our analysis therefore clarifies the role of the trace anomaly in the diffeomorphism anomaly approach cite{wilczek, isowilczek, shailesh, shailesh2, sunandan, sunandan10, rabin10} to the Hawking radiation.
