In the first part of this paper, we show that the Cauchy problem for wave propagation in some static spacetimes presenting a singular timelike boundary is well-posed, if we only require the waves to have finite energy, although no boundary condition is required. This feature does not come from essential self-adjointness, which is false in these cases, but from a different phenomenon that we call the alternative well-posedness property, whose origin is due to the degeneracy of the metric components near the boundary. Beyond these examples, in the second part, we characterize the type of degeneracy which leads to this phenomenon.
Classical and Quantum Gravity
- Pub Date:
- November 2010
- General Relativity and Quantum Cosmology;
- Mathematical Physics;
- Mathematics - Spectral Theory
- 34 pages, 3 figures. Accepted for publication in Class. Quantum Grav