Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2007-09-20
Gen.Rel.Grav.41:1459-1473,2009
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
8 pages
Scientific paper
10.1007/s10714-008-0714-5
We present the exact solution of Einstein's equation corresponding to a static and plane symmetric distribution of matter with constant positive density located below $z=0$. This solution depends essentially on two constants: the density $\rho$ and a parameter $\kappa$. We show that this space-time finishes down below at an inner singularity at finite depth. We match this solution to the vacuum one and compute the external gravitational field in terms of slab's parameters. Depending on the value of $\kappa$, these slabs can be attractive, repulsive or neutral. In the first case, the space-time also finishes up above at another singularity. In the other cases, they turn out to be semi-infinite and asymptotically flat when $z\to\infty$. We also find solutions consisting of joining an attractive slab and a repulsive one, and two neutral ones. We also discuss how to assemble a "gravitational capacitor" by inserting a slice of vacuum between two such slabs.
No associations
LandOfFree
Infinite slabs and other weird plane symmetric space-times with constant positive density does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Infinite slabs and other weird plane symmetric space-times with constant positive density, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Infinite slabs and other weird plane symmetric space-times with constant positive density will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-518304