TL;DR
This paper explores the concept of time within the canonical formulation of gravity, proposing a method to define time consistently by fixing the lapse function and eliminating the shift vector.
Contribution
It introduces a hypersurface orthogonal foliation that removes arbitrariness in the lapse function and simplifies the shift vector, enabling a clearer definition of time in gravitational theories.
Findings
A consistent definition of time in canonical gravity is achieved.
The approach simplifies the mathematical structure of the gravitational field.
Potential implications for quantum gravity formulations.
Abstract
The concept of time is discussed in the context of the canonical formulation of the gravitational field. Using a hypersurface orthogonal foliation, the arbitrariness of the lapse function is eliminated and the shift vector vanishes, allowing a consistent definition of time.
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Taxonomy
TopicsCosmology and Gravitation Theories · Relativity and Gravitational Theory · Black Holes and Theoretical Physics