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

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

2009-10-28

arxiv.org/abs/0910.5439v2

Class. Quantum Grav.27:215016, 2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

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

Scientific paper

10.1088/0264-9381/27/21/215016

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.

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