  In the context of guage/gravity duality, we investigate the central charges
of a number of 2-dimensional conformal field theories (CFTs) that might live on
the boundary of some 3-dimensional (3D) toy models of gravity, from the
thermodynamics aspect of the black holes. For many black hole solutions, the
entropy product of the inner Cauchy and outer event horizons is universal (mass
independent). It is proposed that for these solutions, the central charges of
the left- and right-moving sectors of the dual CFTs should be the same and one
may read the central charges from the universal entropy product. This provides
strong motivations for investigating this prescription for BTZ and Warped
AdS$_{3}$ black holes in a number of 3D gravity theories and we will show that
the proposal works truly. One striking result of our analysis is that if the
entropy product is not universal in any theory of 3D gravity, then the left and
right central charges are not equal.
