Conformally mapped black hole effect in elastic curved continuum

TL;DR

This paper demonstrates a novel elastic continuum approach to mimic black hole effects using conformal mapping, enabling highly confined energy and timing delays around a singularity, with potential applications in sensing and energy harvesting.

Contribution

It introduces a conformal mapping method in elastic media to simulate black hole phenomena, offering a less restrictive alternative to traditional models and establishing a framework for designing elastic analogs of gravitational effects.

Findings

Numerical and experimental validation of energy confinement near the singularity.

Demonstration of timing delays in elastic media analogous to gravitational time dilation.

Establishment of a design framework for elastic analog gravity systems.

Abstract

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.