Intersecting hypersurfaces in AdS and Lovelock gravity
Journal
Journal of Mathematical Physics
Date Issued
September 11, 2006
Author(s)
DOI
10.1063/1.2338143
Abstract
Colliding and intersecting hypersurfaces filled with matter (membranes) are
studied in the Lovelock higher order curvature theory of gravity. Lovelock
terms couple hypersurfaces of different dimensionalities, extending the range
of possible intersection configurations. We restrict the study to constant
curvature membranes in constant curvature AdS and dS background and consider
their general intersections. This illustrates some key features which make the
theory different to the Einstein gravity. Higher co-dimension membranes may lie
at the intersection of co-dimension 1 hypersurfaces in Lovelock gravity; the
hypersurfaces are located at the discontinuities of the first derivative of the
metric, and they need not carry matter.
The example of colliding membranes shows that general solutions can only be
supported by (spacelike) matter at the collision surface, thus naturally
conflicting with the dominant energy condition (DEC). The imposition of the DEC
gives selection rules on the types of collision allowed.
When the hypersurfaces don't carry matter, one gets a soliton-like
configuration. Then, at the intersection one has a co-dimension 2 or higher
membrane standing alone in AdS-vacuum spacetime \emph{without conical
singularities.}
Another result is that if the number of intersecting hypersurfaces goes to
infinity the limiting spacetime is free of curvature singularities if the
intersection is put at the boundary of each AdS bulk.
studied in the Lovelock higher order curvature theory of gravity. Lovelock
terms couple hypersurfaces of different dimensionalities, extending the range
of possible intersection configurations. We restrict the study to constant
curvature membranes in constant curvature AdS and dS background and consider
their general intersections. This illustrates some key features which make the
theory different to the Einstein gravity. Higher co-dimension membranes may lie
at the intersection of co-dimension 1 hypersurfaces in Lovelock gravity; the
hypersurfaces are located at the discontinuities of the first derivative of the
metric, and they need not carry matter.
The example of colliding membranes shows that general solutions can only be
supported by (spacelike) matter at the collision surface, thus naturally
conflicting with the dominant energy condition (DEC). The imposition of the DEC
gives selection rules on the types of collision allowed.
When the hypersurfaces don't carry matter, one gets a soliton-like
configuration. Then, at the intersection one has a co-dimension 2 or higher
membrane standing alone in AdS-vacuum spacetime \emph{without conical
singularities.}
Another result is that if the number of intersecting hypersurfaces goes to
infinity the limiting spacetime is free of curvature singularities if the
intersection is put at the boundary of each AdS bulk.
Subjects