https://doi.org/10.1140/epjp/s13360-025-06610-8
Regular Article
Connection stability of vector fields with astrophysical application to the einstein-vlasov system
1
Department of Pure Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran
2
SUNY Polytechnic Institute, 13502, Utica, New York, USA
3
International Institute for Applicable Mathematics and Information Sciences, B. M. Birla Science Centre, 500063, Adarshnagar, Hyderabad, India
Received:
28
May
2025
Accepted:
30
June
2025
Published online:
19
July
2025
In this paper we present a method for considering the stability of smooth vector fields on a smooth manifold which may not be compact. We show that these kind of stability which is called “connection stability” is equivalent to the structural stability in the case of compact manifolds. We prove if X is a connection stable vector field, then any multiplication of it by a nonzero scalar is also a connection stable vector field. We present an example of a connection stable vector field on a noncompact manifold, and we also show that harmonic oscillator is not a connection stable vector field. We present a technique to prove a class of vector fields are not connection stable. As a concrete physical example, we will apply the analysis to the Einstein-Vlasov system in an astrophysical context in which we propose an approach that could, in principle and partially, help to understand the problem of galaxy rotation curves.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
