Nonuniqueness of Representations of Wave Equations in Lorentzian Space-Times

2012/11/19 by Horst R. Beyer, Horst Reinhard Beyer, Beyer, Horst Reinhard
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #gr-qc #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1211.4426

arxiv created 2012/11/19 · openalex publication_date 2012/11/19 · arxiv updated 2012/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Wave equations on space-times of low regularity: Existence results and regularity theory in the framework of generalized function algebras
• Counterexamples to inverse problems for the wave equation
• Wave Equations on Lorentzian Manifolds and Quantization
• On Solutions to the Wave Equation on Non-globally Hyperbolic Manifold
• An inverse boundary value problem for a semilinear wave equation on Lorentzian manifolds