Probing Black Hole Thermal Effects in the Dual CFT via Wave Packets

We investigate how the gravitational effects of a black hole manifest themselves as thermal behavior in the dual finite-temperature conformal field theory (CFT). In the holographic framework of AdS/CFT, we analyze a wave packet propagating into a black hole geometry in the bulk by computing three-point functions of a scalar primary operator in the boundary CFT. Our setup captures thermal signatures such as exponential damping of the expectation value, which are absent at zero-temperature. This provides a concrete and analytically tractable example of how black hole physics can be probed from the CFT side.