Journal of Nonlinear Mathematical Physics

Volume 11, Issue 3, August 2004, Pages 297 - 324

A Holomorphic Point of View about Geodesic Completeness

Authors
Claudio Meneghini
Corresponding Author
Claudio Meneghini
Received 11 April 2003, Accepted 25 February 2004, Available Online 1 August 2004.
DOI
10.2991/jnmp.2004.11.3.4How to use a DOI?
Abstract

We propose to apply the idea of analytical continuation in the complex domain to the problem of geodesic completeness. We shall analyse rather in detail the cases of analytical warped products of real lines, these ones in parallel with their complex counterparts, and of Clifton-Pohl torus, to show that our definition sheds a bit of new light on the behaviour of 'singularities' of geodesics in space-time. We also show that some geodesics, which 'end' at finite time in the classical sense, can be naturally continued besides their ends. As a matter of fact, complex metrics naturally show a meromorphic behaviour, or a degenerating one, so we shall study also this fact in detail.

Copyright
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
11 - 3
Pages
297 - 324
Publication Date
2004/08/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.2991/jnmp.2004.11.3.4How to use a DOI?
Copyright
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Claudio Meneghini
PY  - 2004
DA  - 2004/08/01
TI  - A Holomorphic Point of View about Geodesic Completeness
JO  - Journal of Nonlinear Mathematical Physics
SP  - 297
EP  - 324
VL  - 11
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2004.11.3.4
DO  - 10.2991/jnmp.2004.11.3.4
ID  - Meneghini2004
ER  -