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Mat. Zametki, 2019, Volume 106, Issue 1, Pages 115–133 (Mi mz12086)  

Causal Properties of Fibered Space-Time

E. I. Yakovleva, T. A. Goncharb

a National Research University "Higher School of Economics", Moscow
b Lobachevski State University of Nizhni Novgorod

Abstract: On the space of a principal bundle, a Lorentzian metric and a time orientation are given that are invariant with respect to the action of the structure group. These objects form a fibered space-time and, in the case of spacelike fibers, induce the same structures on the base. The following causality conditions are discussed: chronology, causality, stable and strong causality, and global hyperbolicity. It is proved that if the base space-time satisfies one of the above conditions, then so does the fibered space-time.

Keywords: principal bundle, $G$-connection, Lorentzian manifold, space-time, causality condition.

Funding Agency Grant Number
HSE Basic Research Program
Russian Foundation for Basic Research 16-01-00312а
The work was completed in the framework of the Basic Research Program of the National Research University Higher School of Economics in 2019 and financially supported by the Russian Foundation for Basic Research under grant 16-01-00312a.

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/mzm12086

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English version:
Mathematical Notes, 2019, 106:1, 118–132

Bibliographic databases:

UDC: 514.762+514.764.2+514.82
Received: 11.06.2018
Revised: 12.09.2018

Citation: E. I. Yakovlev, T. A. Gonchar, “Causal Properties of Fibered Space-Time”, Mat. Zametki, 106:1 (2019), 115–133; Math. Notes, 106:1 (2019), 118–132

Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm12086
  • http://mi.mathnet.ru/eng/mz/v106/i1/p115

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