A classification of spherically symmetric self-similar dust models
| dc.creator | Carr, B. J. | |
| dc.date | 2000-03-02 | |
| dc.date.accessioned | 2026-07-07T11:08:37Z | |
| dc.date.available | 2026-07-07T11:08:37Z | |
| dc.description | We classify all spherically symmetric dust solutions of Einstein's equations which are self-similar in the sense that all dimensionless variables depend only upon $z\equiv r/t$. We show that the equations can be reduced to a special case of the general perfect fluid models with equation of state $p=αμ$. The most general dust solution can be written down explicitly and is described by two parameters. The first one (E) corresponds to the asymptotic energy at large $|z|$, while the second one (D) specifies the value of z at the singularity which characterizes such models. The E=D=0 solution is just the flat Friedmann model. The 1-parameter family of solutions with z>0 and D=0 are inhomogeneous cosmological models which expand from a Big Bang singularity at t=0 and are asymptotically Friedmann at large z; models with E>0 are everywhere underdense relative to Friedmann and expand forever, while those with E<0 are everywhere overdense and recollapse to a black hole containing another singularity. The black hole always has an apparent horizon but need not have an event horizon. The D=0 solutions with z<0 are just the time reverse of the z>0 ones. The 2-parameter solutions with D>0 again represent inhomogeneous cosmological models but the Big Bang singularity is at $z=-1/D$, the Big Crunch singularity is at $z=+1/D$, and any particular solution necessarily spans both z<0 and z>0. While there is no static model in the dust case, all these solutions are asymptotically ``quasi-static'' at large $|z|$. As in the D=0 case, the ones with $E \ge 0$ expand or contract monotonically but the latter may now contain a naked singularity. The ones with E<0 expand from or recollapse to a second singularity, the latter containing a black hole. | |
| dc.description | 30 pages, 4 figures available from author, to appear in PRD | |
| dc.identifier | https://arxiv.org/abs/gr-qc/0003007 | |
| dc.identifier | http://arxiv.org/abs/gr-qc/0003007 | |
| dc.identifier | Phys.Rev.D62:044022,2000 | |
| dc.identifier | doi:10.1103/PhysRevD.62.044022 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/190192 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.title | A classification of spherically symmetric self-similar dust models | |
| dc.type | text |