### Abstract

The local extendibility of causal geodesically incomplete space-times is examined. It is shown that for a space-time including an incomplete inextendible causal geodesic curve γ there exists a particular C^{k} (resp. C^{k-}) local extension provided that the curvature and its covariant derivatives are uniformly bounded up to order k+1 (resp. k) in a synchronized frame field along a family of causal geodesics in some neighborhood of a final segment of γ and the strong causality condition is satisfied locally.

Original language | English |
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Pages (from-to) | 2448-2464 |

Number of pages | 17 |

Journal | Journal of Mathematical Physics |

Volume | 34 |

Issue number | 6 |

Publication status | Published - 1993 |

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### ASJC Scopus subject areas

- Organic Chemistry

### Cite this

**Space-time extensions I.** / Rácz, I.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 34, no. 6, pp. 2448-2464.

}

TY - JOUR

T1 - Space-time extensions I

AU - Rácz, I.

PY - 1993

Y1 - 1993

N2 - The local extendibility of causal geodesically incomplete space-times is examined. It is shown that for a space-time including an incomplete inextendible causal geodesic curve γ there exists a particular Ck (resp. Ck-) local extension provided that the curvature and its covariant derivatives are uniformly bounded up to order k+1 (resp. k) in a synchronized frame field along a family of causal geodesics in some neighborhood of a final segment of γ and the strong causality condition is satisfied locally.

AB - The local extendibility of causal geodesically incomplete space-times is examined. It is shown that for a space-time including an incomplete inextendible causal geodesic curve γ there exists a particular Ck (resp. Ck-) local extension provided that the curvature and its covariant derivatives are uniformly bounded up to order k+1 (resp. k) in a synchronized frame field along a family of causal geodesics in some neighborhood of a final segment of γ and the strong causality condition is satisfied locally.

UR - http://www.scopus.com/inward/record.url?scp=22244482115&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=22244482115&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:22244482115

VL - 34

SP - 2448

EP - 2464

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 6

ER -