相关论文: The legacy of ADM

In 1945 Einstein concluded that [1]: "The present theory of relativity is based on a division of physical reality into a metric field (gravitation) on the one hand, and into an electromagnetic field and matter on the other hand. In reality…

We employ the Arnowitt-Deser-Misner formalism to study the renormalization group flow of gravity minimally coupled to an arbitrary number of scalar, vector, and Dirac fields. The decomposition of the gravitational degrees of freedom into a…

General Relativity (GR) revolutionized the way we thought about gravity. After briefly describing the key successes of GR and its impact, I will discuss the major conceptual challenges it faces today. I conclude by outlining the prospective…

The higher dimensional Quantum General Relativity of a Riemannian manifold being an embedded space in a space-time being a Lorentzian manifold is investigated. The model of quantum geometrodynamics, based on the Wheeler-DeWitt equation…

I discuss Albert Einstein's 1914 review paper, "The Formal Foundation of the General Theory of Relativity" from two points of view: the main elements in the paper that appear to have led to the downfall of the Einstein-Grossman theory; and…

In the early 80's, Alain Quilliot presented an approach of ordered sets and graphs in terms of metric spaces, where instead of positive real numbers, the values of the distance are elements of an ordered monoid equipped with an involution.…

Higher dimensional space-time models provide us an alternative interpretation of nature, and give us different dynamical aspects than the traditional four-dimensional space-time models. Motivated by such recent interests, especially for…

We show that the concept of the ADM mass in general relativity can be understood as the limit of the total mean curvature plus the total defect of dihedral angle of the boundary of large Riemannian polyhedra. We also express the…

The intermediate stage of the development of general relativity is inseparable of Marcel Grossmann's mathematical assistance. Einstein acknowledges Grossmann's help during 1912-1914 to the development of general relativity. In fact, as with…

General relativity marked the beginning of modern cosmology and it has since been at the centre of many of the key developments in this field. In the present review, we discuss the general-relativistic dynamics and perturbations of the…

I show in this letter that it is possible to solve some of the constraints of the $SO(3)$-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…

We review the physics at the end of the nineteenth century and summarize the process of the establishment of Special Relativity by Albert Einstein in brief. Following in the giant's footsteps, we outline the scientific method which helps to…

The 3+1 (ADM) formulation of General Relativity is used in, for example, canonical quantum gravity and numerical relativity. Here we present a 3+1 decomposition of the minimal Standard-Model Extension gravity Lagrangian. By choosing the…

The nature of gravity is fundamental to our understanding of our own solar system, the galaxy and the structure and evolution of the Universe. Einstein's general theory of relativity is the standard model that is used for almost ninety…

This is an English translation of the Italian version of an encyclopedia chapter that appeared in the Italian Encyclopedia of the Physical Sciences, edited by Bruno Bertotti (1994). Following requests from colleagues we have decided to make…

This is a review of the chrono-geometrical structure of special and general relativity with a special emphasis on the role of non-inertial frames and of the conventions for the synchronization of distant clocks. ADM canonical metric and…

This lecture will present a review of the past and present tests of the General Relativity theory. The essentials of the theory will be recalled and the measurable effects will be listed and analyzed. The main historical confirmations of…

Einstein established the theory of general relativity and the corresponding field equation in 1915 and its vacuum solutions were obtained by Schwarzschild and Kerr for, respectively, static and rotating black holes, in 1916 and 1963,…

A new spinorial strategy for the construction of geometric inequalities involving the Arnowitt-Deser-Misner (ADM) mass of black hole systems in general relativity is presented. This approach is based on a second order elliptic equation (the…

A brief outline of the history of the discrepancies within Newtonian mechanics at the end of the nineteenth century is given. The framework of general relativity is described briefly and the famous 'tests' of general relativity are…