Mathematical Clarification of General Relativistic Variational Principles
Andr\'as L\'aszl\'o
TL;DR
This paper introduces a mathematically rigorous global approach to variational principles in general relativity, aiming to facilitate proofs of global existence theorems for field solutions.
Contribution
It develops a precise global framework for variational principles in general relativistic theories, addressing limitations of traditional local methods.
Findings
Provides a global variational framework for general relativity
Highlights issues with classic local approaches
Lays groundwork for future global existence proofs
Abstract
In this paper a mathematically precise global (i.e. not the usual local) approach is presented to the variational principles of general relativistic classical field theories. Problems of the classic (usual) approaches are also discussed in comparison. The aim of developing a global approach is to provide a possible tool for future efforts on proving global existence theorems of field theoretical solutions.
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Taxonomy
TopicsCosmology and Gravitation Theories · Pulsars and Gravitational Waves Research · Relativity and Gravitational Theory