A Holomorphic Point of View about Geodesic Completeness

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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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  -