Infinite slabs and other weird plane symmetric space-times with constant positive density

RICARDO E. GAMBOA SARAVÍ

GENERAL RELATIVITY AND GRAVITATION

Springer

Año: 2008 vol. 41

0001-7701

We present  the exact  solution of Einstein´s equationcorresponding to a static and plane symmetric distribution ofmatter with constant positive density located below $z=0$. Thissolution depends essentially on two constants: the density $ ho$and a parameter $kappa$. We show that these space-times finishdown below at an inner singularity at finite depth. We match thissolution to the vacuum one and compute the external gravitationalfield in terms of  slab´s parameters. Depending on the value of$kappa$, these slabs can be attractive, repulsive or neutral. Inthe first case, the space-time also finishes up above at an empty repellingsingular boundary.  In  the other cases,  they turn out to besemi-infinite and  asymptotically flat when $z ightarrowinfty$. We also find solutions consisting of  joining   an attractive slaband a repulsive one, and two neutral ones. We also discuss how toassemble a ``gravitational capacitor" by inserting a slice ofvacuum between two such slabs.