Introduction to Hamiltonian formulation of general relativity and homogeneous cosmologies

Plebanski Formulation of General Relativity: A Practical Introduction

We give a pedagogical introduction into an old, but unfortunately not very well-known formulation of GR in terms of self-dual two-forms due to Plebanski. Our presentation is rather explicit in that we show how the familiar textbook solutions: Schwarzschild, Volkoff-Oppenheimer, as well as those describing the Newtonian limit, graviton and homogeneous isotropic Universe can be obtained within th...

Lagrangian Formulation of General Relativity

Hyperbolic Formulation of General Relativity

Einstein’s theory, viewed mathematically as a system of second-order partial differential equations for the metric, is not a hyperbolic system without modification and is not manifestly well-posed, though physical information propagates at the speed of light. A well-posed hyperbolic system admits unique solutions which depend continuously on the initial data and seems to be required for robust,...

Introduction to Tensor Calculus for General Relativity

There are three essential ideas underlying general relativity (GR). The first is that spacetime may be described as a curved, four-dimensional mathematical structure called a pseudo-Riemannian manifold. In brief, time and space together comprise a curved fourdimensional non-Euclidean geometry. Consequently, the practitioner of GR must be familiar with the fundamental geometrical properties of c...

Invariant Hamiltonian Quantization of General Relativity

The quantization of General Relativity invariant with respect to time-reparametrizations is considered. We construct the Faddeev-Popov generating functional for the unitary perturbation theory in terms of invariants of the kinemetric group of diffeomorphisms of a frame of reference as a set of Einstein’s observers with the equivalent Hamiltonian description (t = t(t), x = x(t, x, x, x)). The al...