An alternative well-posedness property and static spacetimes with naked singularities

Abstract

In the first part of this paper, we show that the Cauchy problem for wave propagation in some static spacetimes presenting a singular time-like boundary is well posed, if we only demand 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.

34 pages, 3 figures. Accepted for publication in Class. Quantum Grav

References in corpus (6)

• Dynamics in Stationary, Non-Globally Hyperbolic Spacetimes
• Scalar waves on a naked-singularity background
• Static plane symmetric relativistic fluids and empty repelling singular boundaries
• The white wall, a gravitational mirror
• Infinite slabs and other weird plane symmetric space-times with constant positive density
• The Gravitational Field of a Plane Slab

Cited by in corpus (2)

• Higher-dimensional perfect fluids and empty singular boundaries
• Empty singularities in higher-dimensional Gravity