Related papers: Solving the Constraints of General Relativity
Starting from a Hamiltonian description of four dimensional general relativity in presence of a cosmological constant we perform the program of canonical quantisation. This is done using complex Ashtekar variables while keeping the…
We study the Ashtekar formulation of linear gravity starting from the ADM first order action for the non linear theory, linearizing it, and performing a canonical transformation that coordinatizes the phase space in terms of the already…
We use a trick similar to Weinberg's for adiabatic modes, in a Manton approximation for general relativity on manifolds with spatial boundary. This results in a description of the slow-time dependent solutions as null geodesics on the space…
It is shown that the Wheeler DeWitt constraint of canonical gravity coupled to Klein Gordon scalar fields and expressed in terms of Ashtekar's variables admits formal solutions which are parametrized by loops in the three dimensional…
In this paper we provide an action related to a certain sector of general relativity where the algebra of Hamiltonian constraints forms a first class system. This action is a Dirac-consistent stand-alone action with two physical degrees of…
In the search for exact solutions to Einstein's field equations the main simplification tool is the introduction of spacetime symmetries. Motivated by this fact we develop a method to write the field equations for general matter in a form…
The purpose of this article is to draw attention to some fundamental issues in General Relativity. It is argued that these deep issues cannot be resolved within the standard approach to general relativity that considers {\em every} solution…
We show that a reformulation of the ADM equations in general relativity, which has dramatically improved the stability properties of numerical implementations, has a direct analogue in classical electrodynamics. We numerically integrate…
In general relativity, systems of spinning classical particles are implemented into the canonical formalism of Arnowitt, Deser, and Misner [1]. The implementation is made with the aid of a symmetric stress-energy tensor and not a…
We discuss the application of the method of the gaugeless Hamiltonian reduction to general relativity. This method is based on explicit resolving the global part of the energy constraint and on identification of one of the metric components…
Using the ADM formalism, we demonstrate that the Hamiltonian formulation of Quantum Gravity is exactly in the form of a worldline (WL) formalism in the superspace. We then show that the Keldysh partition function reduces to the partition…
This paper addresses the question of whether Witten's proof of positive ADM energy for classical general relativity can be extended to give a proof of positive energy for a non-perturbative quantization of general relativity. To address…
This PhD thesis contains a collection of work related to the algebraic classification of spacetimes in higher dimensions, including an up-to-date review of various aspects of the field. The work discussed includes the higher-dimensional…
The classic Alternating Direction Method of Multipliers (ADMM) is a popular framework to solve linear-equality constrained problems. In this paper, we extend the ADMM naturally to nonlinear equality-constrained problems, called neADMM. The…
The alternating direction method of multipliers (ADMM) has been widely used for solving structured convex optimization problems. In particular, the ADMM can solve convex programs that minimize the sum of $N$ convex functions with $N$-block…
As basic variables in general relativity (GR) are chosen antisymmetric connection and bivectors - bilinear in tetrad area tensors subject to appropriate (bilinear) constraints. In canonical formalism we get theory with polinomial…
In a recent work we derived the kinematic Hamiltonian and primary constraints of the new general relativity class of teleparallel gravity theories and showed that these theories can be grouped in 9 classes, based on the presence or absence…
The present paper shows that general relativity in the Arnowitt-Deser-Misner formalism admits a BV-BFV formulation. More precisely, for any $d + 1 \not= 2$ (pseudo-) Riemannian manifold M with space-like or time-like boundary components,…
This Thesis concerns a thin fluid shell embedded in its own gravitational field. The starting point is a work of Hajicek and Kijowski, where the hamiltonian formalism for shell(s) (with no symmetry) in Einstein gravity is developed. An open…
In the MacDowell-Mansouri formulation of general relativity, the spin connection and coframe variables are incorporated into a single Lie algebra-valued connection called the MacDowell-Mansouri connection, $\omega$. From the curvature form…