Canonical superenergy density and local gravitational stability / Gęstość kanonicznej super energii a lokalna stabilność grawitacyjna
Journal Title: Bulletin de la Société des sciences et des lettres de Łódź, Série: Recherches sur les déformations - Year 2016, Vol 0, Issue 2
Abstract
In the framework of general relativity one has very hard problem with gravitational energy density, not satisfactorily solved up to now. It is a consequence of the Einstein Equivalence Principle. To avoid the problem we have introduced in past the canonical su- perenergy tensors. It turned out that these tensors give a very good tool to local, and in special cases also to global, analysis of the gravitational field in general relativity (See pa- pers cited in References). Here we propose a new application of the canonical superenergy density. Namely, we propose to use this density to study local gravitational stability of the solutions to the Einstein equations. Our proposition follows the procedure of finding the stable minima of the interior energy U for a thermodynamical system. By using ther- modynamical analogy we have formulated and proved Proposition from which it follows the Conclusion which says that when the total superenergy density, matter and gravi- tation, is positive-definite, then the solution can be gravitationally stable, i.e., it can be stable under small metric perturbations. Contrary, when the total superenergy density is negative-definite, then the solution cannot be gravitationally stable.We give many examples of application of the Conclusion.
Authors and Affiliations
Janusz Garecki
Keywords
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