  It is known that the $(a,c)$ central charges in four-dimensional CFTs are
linear combinations of the three independent OPE coefficients of the
stress-tensor three-point function. In this paper, we adopt the holographic
approach using AdS gravity as an effect field theory and consider higher-order
corrections up to and including the cubic Riemann tensor invariants. We derive
the holographic central charges and OPE coefficients and show that they are
invariant under the metric field redefinition. We further discover a hidden
relation among the OPE coefficients that two of them can be expressed in terms
of the third using differential operators, which are the unit radial vector and
the Laplacian of a four-dimensional hyperbolic space whose radial variable is
an appropriate length parameter that is invariant under the field redefinition.
Furthermore, we prove that the consequential relation $c=1/3 \ell_{\rm
eff}\partial a/\partial\ell_{\rm eff}$ and its higher-dimensional
generalization are valid for massless AdS gravity constructed from the most
general Riemann tensor invariants.
