相关论文: Integration in General Relativity

A new class of modified theory of gravity is introduced where the volume form becomes dynamical. This approach is motivated by unimodular gravity and can also be related to Brans-Dicke theory. On the level of the action, the only change…

The mathematical theory of gravitational lensing has revealed many generic and global properties. Beginning with multiple imaging, we review Morse-theoretic image counting formulas and lower bound results, and complex-algebraic upper bounds…

This is an elementary introduction to basic tools of supersymmetry: the spacetime symmetries, gauge theory and its application in gravity, spinors and superalgebras. Special attention is devoted to conformal and anti-de Sitter algebras.

I give a very brief introduction to the use of effective field theory techniques in quantum calculations of general relativity. The gravitational interaction is naturally organized as a quantum effective field theory and a certain class of…

In this expository paper we want to give a brief introduction, with few key references for further reading, to the inner functioning of the new and successfull algorithms of Deep Learning and Geometric Deep Learning with a focus on Graph…

This is an introduction into the problem of how to set up black hole initial-data for the matter-free field equations of General Relativity. The approach is semi-pedagogical and addresses a more general audience of astrophysicists and…

The geometrical nature of gravity emerges from the universality dictated by the equivalence principle. In the usual formulation of General Relativity, the geometrisation of the gravitational interaction is performed in terms of the…

General Relativity is the modern theory of gravitation. It has replaced the newtonian theory in the description of the gravitational phenomena. In spite of the remarkable success of the General Relativity Theory, the newtonian gravitational…

Relying on a fundamental empirical identity of heavy and inertial mass it is proposed to bring a status of general theory of relativity (GTR) of Einstein up to a level of Unified Field Theory. To do this, a thoroughgoing revision of…

Algebras of generalized functions offer possibilities beyond the purely distributional approach in modelling singular quantities in non-smooth differential geometry. This article presents an introductory survey of recent developments in…

A new geometric interpretation for General Relativity (GR) is proposed. We show that in the presence of an arbitrary affine connection, the gravitational field is described as nonmetricity of the affine connection. An affine connection can…

Standard pedagogy treats topics in general relativity (GR) in terms of tensor formulations in curved space-time. Although mathematically straightforward, the curved space-time approach can seem abstruse to beginning students due to the…

An analysis of composite inertial motion (relativistic sum) within the framework of special relativity leads to the conclusion that every translational motion must be the symmetrically composite relativistic sum of a finite number of quanta…

These lecture notes are intended as a guide to Graduate level readers that are already familiar with basic General Relativity. They present in a concise way some advanced concepts and problems encountered in the study of gravitation. In…

An introduction to loop quantum gravity is given, focussing on the fundamental aspects of the theory, different approaches to the dynamics, as well as possible future directions. It is structured in five lectures, including exercises, and…

This thesis is devoted to the study of gravitational theories which can be seen as modifications or generalisations of General Relativity. The motivation for considering such theories, stemming from Cosmology, High Energy Physics and…

This paper gives a summary of the author's works concerning the emergent general relativity in a particular class of tensor models, which possess Gaussian classical solutions. In general, a classical solution in a tensor model may be…

This tutorial aims to provide an intuitive introduction to Gaussian process regression (GPR). GPR models have been widely used in machine learning applications due to their representation flexibility and inherent capability to quantify…

The article presents some aspects on the use of computer in teaching general relativity for undergraduate students with some experience in computer manipulation. The article presents some simple algebraic programming (in REDUCE+EXCALC…

This review is an up-to-date account of the use of numerical relativity to study dynamical, strong-gravity environments in a cosmological context. First, we provide a gentle introduction into the use of numerical relativity in solving…