The Square of Area Reality Constraint in Classical General Relativity
Year: 2005
Type: preprint
Abstract: Recently an area reality constraint has been introduced in the context of the spin foam models of general relativity. The idea is that the Barrett-Crane models of 4D real general relativity theories of all signatures are related to the SO(4, C) Barrett-Crane model through the square of area reality constraint. Here I would like to explore this relationship at the classical level. The classical continuum equivalent of the squares of the areas of triangles of a simplicial manifold is the area metric. First I review the Plebanski theory of the SO(4, C) general relativity. Then I modify the theory by adding a Lagrange multiplier to impose the area metric reality condition. The area metric is real iff a non-degenerate metric is real or imaginary. I investigate two types of action: Complex and Real. All the non-trivial solutions of the field equations of the theory with the complex action correspond to real general relativity. Half the non-trivial solutions of the field equations of the theory with the real action correspond to real general relativity. 1
Source: arXiv (Cornell University)
Author: Suresh K Maran
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2787262746