Solving the Constraints of General Relativity
J. Fernando Barbero
TL;DR
This paper demonstrates a method to solve certain constraints in the $SO(3)$-ADM formalism of general relativity by adapting techniques from the Ashtekar variables approach, highlighting benefits of the ADM framework.
Contribution
It introduces a novel approach to solving constraints in the ADM formalism inspired by Ashtekar variables, providing new insights into Hamiltonian formulations of general relativity.
Findings
Successfully solves some $SO(3)$-ADM constraints using Ashtekar-inspired methods
Highlights advantages of the ADM formalism over other Hamiltonian approaches
Compares the proposed method with existing formulations of general relativity
Abstract
I show in this letter that it is possible to solve some of the constraints of the -ADM formalism for general relativity by using an approach similar to the one introduced by Capovilla, Dell and Jacobson to solve the vector and scalar constraints in the Ashtekar variables framework. I discuss the advantages of using the ADM formalism and compare the result with similar proposals for different Hamiltonian formulations of general relativity.
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