  We present a black hole effect by strategically leveraging a conformal
mapping in elastic continuum with curved-space framework, which is less
stringent compared to a Schwarzschild model transformed to isotropic refractive
index profiles. In the conformal map approach, the 2D point singularity
associated to the black hole effect is accomplished by physical plates with
near-to-zero thickness. The analog gravity around the singularity results in
highly confined energy and lagged timings within a branch cut of the conformal
map. These effects are quantified both numerically and experimentally in
reference to control trials in which the thickness is not modulated. The
findings would deepen our understanding of the elastic analog in mimicking
gravitational phenomena, as well as establish the elastic continuum framework
for developing a generic design recipe in the presence of the index
singularity. Geometric landscapes with elastically curved surfaces would be
applicable in a variety of applications such as sensing, imaging, vibration
isolation, and energy harvesting.
