Inverse hyperbolic problems and optical black holes

TL;DR

This paper presents a geometric approach to inverse hyperbolic problems, applies it to light propagation in moving media, and explores the existence of optical black and white holes affecting inverse problem solutions.

Contribution

It introduces a geometric formulation of inverse hyperbolic problems and analyzes the impact of optical black and white holes on these problems.

Findings

Geometric reformulation of inverse hyperbolic problems

Existence of optical black and white holes in hyperbolic equations

Impact of black/white holes on inverse problem solvability

Abstract

In this paper we give a more geometrical formulation of the main theorem in [E1] on the inverse problem for the second order hyperbolic equation of general form with coefficients independent of the time variable. We apply this theorem to the inverse problem for the equation of the propagation of light in a moving medium (the Gordon equation). Then we study the existence of black and white holes for the general hyperbolic and for the Gordon equation and we discuss the impact of this phenomenon on the inverse problems.