### Abstract

The detailed construction of six Regge spacetimes, each being an approximation to a time symmetric Friedmann dust-filled Universe, are presented. These spacetimes are a generalisation of those originally constructed by Collins and Williams (1973). This paper presents new methods for the subdivision of each Cauchy surface into a set of tetrahedra, for the construction of the general four-dimensional block and for the implementation of the constraints of homogeneity and isotropy. A new action sum for pure dust in a Regge spacetime is also presented. The evolution of the Regge spaces is seen to terminate prior to the full collapse of the Universe. This is shown to occur when the particle horizon for an observer at the centre of one tetrahedron has contracted so as to just touch the vertices of that tetrahedron. It is argued that this is a generic feature and will occur in any Regge spacetime whenever the local curvature becomes too large.

Original language | English |
---|---|

Article number | 023 |

Pages (from-to) | 899-928 |

Number of pages | 30 |

Journal | Classical and Quantum Gravity |

Volume | 4 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1 Dec 1987 |

Externally published | Yes |

### Cite this

*Classical and Quantum Gravity*,

*4*(4), 899-928. [023]. https://doi.org/10.1088/0264-9381/4/4/023

}

*Classical and Quantum Gravity*, vol. 4, no. 4, 023, pp. 899-928. https://doi.org/10.1088/0264-9381/4/4/023

**Friedmann cosmologies via the Regge calculus.** / Brewin, L.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Friedmann cosmologies via the Regge calculus

AU - Brewin, L.

PY - 1987/12/1

Y1 - 1987/12/1

N2 - The detailed construction of six Regge spacetimes, each being an approximation to a time symmetric Friedmann dust-filled Universe, are presented. These spacetimes are a generalisation of those originally constructed by Collins and Williams (1973). This paper presents new methods for the subdivision of each Cauchy surface into a set of tetrahedra, for the construction of the general four-dimensional block and for the implementation of the constraints of homogeneity and isotropy. A new action sum for pure dust in a Regge spacetime is also presented. The evolution of the Regge spaces is seen to terminate prior to the full collapse of the Universe. This is shown to occur when the particle horizon for an observer at the centre of one tetrahedron has contracted so as to just touch the vertices of that tetrahedron. It is argued that this is a generic feature and will occur in any Regge spacetime whenever the local curvature becomes too large.

AB - The detailed construction of six Regge spacetimes, each being an approximation to a time symmetric Friedmann dust-filled Universe, are presented. These spacetimes are a generalisation of those originally constructed by Collins and Williams (1973). This paper presents new methods for the subdivision of each Cauchy surface into a set of tetrahedra, for the construction of the general four-dimensional block and for the implementation of the constraints of homogeneity and isotropy. A new action sum for pure dust in a Regge spacetime is also presented. The evolution of the Regge spaces is seen to terminate prior to the full collapse of the Universe. This is shown to occur when the particle horizon for an observer at the centre of one tetrahedron has contracted so as to just touch the vertices of that tetrahedron. It is argued that this is a generic feature and will occur in any Regge spacetime whenever the local curvature becomes too large.

UR - http://www.scopus.com/inward/record.url?scp=0039763069&partnerID=8YFLogxK

U2 - 10.1088/0264-9381/4/4/023

DO - 10.1088/0264-9381/4/4/023

M3 - Article

VL - 4

SP - 899

EP - 928

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

SN - 0264-9381

IS - 4

M1 - 023

ER -