  Black holes are considered among the most fascinating objects that exist in
our universe, since in the classical formalism nothing, even no light, can
escape from their vicinity due to gravity. The gravitational potential causes
the light to bend towards the hole, which is known by gravitational lensing.
Here we present a synthetic realization of this phenomenon in a lab-scale
two-dimensional network of mechanical circuits, based on analogous condensed
matter formalism of Weyl semimetals with inhomogeneous nodal tilt profiles.
Some of the underlying network couplings turn out as unstable and
non-reciprocal, and are implemented by embedded active feedback interactions in
an overall stabilized structure. We demonstrate the lensing by propagating
mechanical wavepackets through the network with a programmed funnel-like
potential, achieving wave bending towards the circle center. We then
demonstrate the versatility of our platform by reprogramming it to mimic
quantum tunneling of particles through the event horizon, known by Hawking
radiation, achieving an exceptional correspondence to the original mass loss
rate within the hole. The network couplings and the potential can be further
reprogrammed to realize other curvatures and associated relativistic phenomena.
