What is it about?
Observables are measurable quantities of a theory describing the physics of the theory. We obtain such quantities in terms of the natural gravitational variables, connection and curvature. The result is that we obtain, via the connection observable, a relation between local energy and momentum for a wide class of gravitational fields. Obtaining such a dispersion relation between local energy and momentum has proved to be particularly difficult in General Relativity and is bound to play a significant role in quantising the case of gravity considered.
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Why is it important?
We obtain a relation between energy and momentum in the case of Gravity considered that is a Klein-Gordon equation for Gravity. This is an equation very well studied in particle physics and therefore will help towards quantizing the case of gravity fields considered. Also such an equation for local energy and momentum could prove of use in classical gravity considerations.
Perspectives
The research addresses directly an element missing in General Relativity that is local energy and momentum densities in the vacuum case which are shown to obey a Klein-Gordon equation
Dr Panagiotis Kordas
Institute of Physics
Read the Original
This page is a summary of: Observables in terms of connection and curvature variables for Einstein’s equations with two commuting Killing vectors, Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences, November 2015, Royal Society Publishing,
DOI: 10.1098/rspa.2015.0350.
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