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Einstein constraint equations in Ashtekar form

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dc.contributor.advisor Lemmer G, Prof en
dc.contributor.author Tsima EB en
dc.date.accessioned 2016-09-22T11:54:25Z
dc.date.available 2016-09-22T11:54:25Z
dc.date.submitted 1996 en
dc.identifier.uri http://hdl.handle.net/20.500.11892/141890
dc.description.abstract The usual phase space of general relativity is described by pairs of variables (q<sub>ab'</sub>p<sup>ab</sup>) defined on a three-dimensional manifold &Sigma;. Not all of these variables are "dynamical variabales" i.e. not all of them have physical content - there are so-called "constraint equations". Unfortunately, in terms of these variables, Einstein constraint equations take an extremely complicated form. However, Ashtekar has recently introduced "canonically conjugate" variables in terms of which the constraints become polynomials. This removes the severe nonlinearity which has been thought to be an inevitable nature of general relativity.<br><br> Ashtekar variables are found to be the density-valued soldering forms &tilde;&sigma;<sup>a</sup><sub>A</sub>[a above A]<sup>B</sup> and certain spin connection 1-forms <sup>&plusmn;</sup> A<sub>a</sub><sup>B</sup><sub>A</sub>[B above A]. The Einstein constraints are at worst quadratic in each of the variables &tilde;&sigma;<sup>a</sup><sub>A</sub><sup>B</sup> [a above A] and <sup>&plusmn;</sup>A<sub>a</sub><supB</sup><sub>A</sub>[B above A]. This simple form of the constraints provides a natural imbedding of the constraint surface in the phase space of Einstein's theory into that of Yang-Mills phase space. en
dc.language English en
dc.subject Mathematics, mathematical statistics and statistics en
dc.subject General en
dc.title Einstein constraint equations in Ashtekar form en
dc.type Masters degree en
dc.description.degree MSc en


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