Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2003-12-04
J.Math.Phys.46:033509,2005
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Scientific paper
10.1063/1.1851603
Generalizing the Lie derivative of smooth tensor fields to distribution-valued tensors, we examine the Killing symmetries and the collineations of the curvature tensors of some distributional domain wall geometries. The chosen geometries are rigorously the distributional thin wall limit of self gravitating scalar field configurations representing thick domain walls and the permanence and/or the rising of symmetries in the limit process is studied. We show that, for all the thin wall spacetimes considered, the symmetries of the distributional curvature tensors turns out to be the Killing symmetries of the pullback of the metric tensor to the surface where the singular part of these tensors is supported. Remarkably enough, for the non-reflection symmetric domain wall studied, these Killing symmetries are not necessarily symmetries of the ambient spacetime on both sides of the wall.
Pantoja Nelson
Sanoja Alberto
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