Related papers: Dynamical and Hamiltonian formulation of General R…
This paper is a rebuttal to Eur. Phys. Jour. Plus 130, 191 (2015), which claims that the results in arXiv:1502.04911 (Ann. Phys. 355, 360 (2015)) are incorrect. For this reason, some of the results in arXiv:1502.04911 have been reviewed and…
As a sequel to (Berman, 2008a), we show that the rotation of the Universe can be dealt by generalised Gaussian metrics, defined in this paper. Robertson-Walker's metric has been employed with proper-time, in its standard applications; the…
Shape dynamics is a reformulation of general relativity, locally equivalent to Einstein's theory, in which the refoliation invariance of the older theory is traded for local scale invariance. Shape dynamics is here derived in a formulation…
This chapter of the proceedings for the Ninth Meeting on CPT and Lorentz Symmetry is dedicated to the Hamiltonian formulation of the minimal gravitational Standard-Model Extension. Some theoretical questions associated with the latter shall…
I provide a very brief sketch of some of Dirac's interests and work in gravity, particularly his Hamiltonian formulation of Einstein's theory and its relation to his earlier research.
A modification of General Relativity that is based on the gravitational Standard-Model Extension and incorporates nondynamical background fields has recently been studied via the ADM formalism. Our objective in this paper is to develop a…
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…
We present a new formulation of the Einstein equations that casts them in an explicitly first order, flux-conservative, hyperbolic form. We show that this now can be done for a wide class of time slicing conditions, including maximal…
This is a review with some comments on the A. Einstein`s 1911 paper, which he published as one of his many attempts of the general theory of relativity. The main point of the idea is to propose a new approach about light and its motion as…
The Hamiltonian formulation of general relativity (GR) is considered in finite space-time and a specific frame of reference given by the diffeo-invariant components of the Fock simplex in terms of the Dirac -- ADM variables. The evolution…
We present a first-order symmetric hyperbolic system in the Ashtekar formulation of general relativity for vacuum spacetime. We add terms from constraint equations to the evolution equations with appropriate combinations, which is the same…
We consider general curvature-invariant modifications of the Einstein-Hilbert action that become important only in regions of extremely low space-time curvature. We investigate the far future evolution of the universe in such models,…
We describe a class of modified gravity theories that deform general relativity in a way that breaks time reversal invariance and, very mildly, locality. The algebra of constraints, local physical degrees of freedom, and their linearized…
It is very likely that the quantum description of spacetime is quite different from what we perceive at large scales, $l\gg (G\hbar/c^3)^{1/2}$. The long wave length description of spacetime, based on Einstein's equations, is similar to the…
There are many complementary approaches to the construction of solutions to the field equations of general relativity. Among these, numerical approximation offers the only possibility to compute a variety of dynamical spacetimes, and so has…
We review the foundations of Einstein's general theory of relativity, discuss recent progress in the tests of relativistic gravity, and present motivations for new generation of high-accuracy gravitational experiments. We discuss the…
Soon after he proposed three classic observational tests for the general theory of relativity, Einstein realised that a consistent description of the universe as a whole provided another important challenge for the theory. In this essay, we…
It is well known that the Einstein-Hilbert action in two dimensions is topological and yields an identically vanishing Einstein tensor. Consequently one is faced with difficulties when formulating a non-trivial gravity model. We present a…
Einstein's equations for general relativity, when viewed as a dynamical system for evolving initial data, have a serious flaw: they cannot be proven to be well-posed (except in special coordinates). That is, they do not produce unique…
Various Hamiltonian formulations of f(R) gravity can be found in the literature. Some authors follow the Ostrogradsky treatment of higher derivative theories and introduce as extra variables first order time derivatives of the metric…