An alternative wellposedness 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 timelike boundary is wellposed, if we only require the waves to have finite energy, although no boundary condition is required. This feature does not come from essential selfadjointness, which is false in these cases, but from a different phenomenon that we call the alternative wellposedness 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.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 November 2010
 DOI:
 10.1088/02649381/27/21/215016
 arXiv:
 arXiv:0910.5439
 Bibcode:
 2010CQGra..27u5016G
 Keywords:

 General Relativity and Quantum Cosmology;
 Mathematical Physics;
 Mathematics  Spectral Theory
 EPrint:
 34 pages, 3 figures. Accepted for publication in Class. Quantum Grav