Energy Conditions and Junction Conditions

Details Energy Conditions and Junction Conditions Energy Conditions and Junction Conditions

2005-05-11

arxiv.org/abs/gr-qc/0505048v2

Phys.Rev.D72:044016,2005

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 pages; v2: minor corrections, brief comments on negative energy spacetimes in sec.4 added

Scientific paper

10.1103/PhysRevD.72.044016

We consider the familiar junction conditions described by Israel for thin timelike walls in Einstein-Hilbert gravity. One such condition requires the induced metric to be continuous across the wall. Now, there are many spacetimes with sources confined to a thin wall for which this condition is violated and the Israel formalism does not apply. However, we explore the conjecture that the induced metric is in fact continuous for any thin wall which models spacetimes containing only positive energy matter. Thus, the usual junction conditions would hold for all positive energy spacetimes. This conjecture is proven in various special cases, including the case of static spacetimes with spherical or planar symmetry as well as settings without symmetry which may be sufficiently well approximated by smooth spacetimes with well-behaved null geodesic congruences.

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