Nonuniqueness of Representations of Wave Equations in Lorentzian Space-Times
General Relativity and Quantum Cosmology
2012-11-20 v1 Mathematical Physics
math.MP
Abstract
This brief note wants to bring to attention that the formulation of physically reasonable initial-boundary value problems for wave equations in Lorentzian space-times is not unique, i.e., that there are inequivalent such formulations that lead to a different outcome of the stability discussion of the solutions. For demonstration, the paper uses the case of the wave equation on the right Rindler wedge in 2-dimensional Minkowski space. The used methods can be generalized to wave equations on stationary globally hyperbolic space-times with horizons in higher dimensions, such as Schwarzschild and Kerr space-times.
Keywords
Cite
@article{arxiv.1211.4426,
title = {Nonuniqueness of Representations of Wave Equations in Lorentzian Space-Times},
author = {Horst Reinhard Beyer},
journal= {arXiv preprint arXiv:1211.4426},
year = {2012}
}