Asian Journal of Mathematics and Computer Research
 

Asian Journal of Mathematics and Computer Research, ISSN No. : 2395-4205 (Print), 2395-4213 (Online), Vol.: 20, Issue.: 1

Original Research Article

ROLE OF TOPOLOGIES IN THE STUDY OF DYNAMICAL ASPECTS OF STABLE AND GENERIC PROPERTIES OF SPACE-TIMES IN GENERAL RELATIVITY

 

R. V. SARAYKAR1* AND SUJATHA JANARDHAN2
1Department of Mathematics, R T M Nagpur University, Nagpur-440033. India.
2Department of Mathematics, St. Francis De Sales College, Nagpur-440006, India.

Abstracts

In [1], the authors have studied stability of certain causal properties of space-times in general relativity. As a continuation of this work, in the present paper, we review and discuss, some more aspects of stability which occur in various situations in the dynamics of general relativity. We argue that not only choice of appropriate topology, but also the nature of perturbation, like metric, matter or initial data, are key factors in deciding whether a property is stable or not. We also study certain properties of space-times which are generic in an appropriate mathematical sense. In particular we argue that Linearization stability of a space-time is a generic property.

Keywords :

Topology on the space of Lorentz metrics; whitney-Cr topology; metric perturbations; linearization stability; generic properties.