TL;DR
This paper reviews the existence and stability of artificial black holes in wave equations within moving media, highlighting their differences from astrophysical black holes and their mathematical properties.
Contribution
It summarizes the author's previous results on the existence and stability of artificial black holes in stationary wave equations in two dimensions and axisymmetric cases.
Findings
Existence of artificial black holes in wave equations
Stability results for these black holes
Analysis in two-dimensional and axisymmetric scenarios
Abstract
We study black holes for the linear hyperbolic equations describing the wave propagation in the moving medium. Such black holes are called artificial since the Lorentz metric associated with the hyperbolic equation does not necessary satisfies the Einstein equations. Artificial black holes also arise when we consider perturbations of the Einstein equations. In this paper we review author's results of [E2] and [E3] on the existence and the stability of black holes for the stationary wave equations in two space dimensions, and in the axisymmetric case.
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Taxonomy
TopicsQuantum Electrodynamics and Casimir Effect · Cosmology and Gravitation Theories · Relativity and Gravitational Theory