Related papers: Integration in General Relativity
This is a brief introduction to general relativity, designed for both students and teachers of the subject. While there are many excellent expositions of general relativity, few adequately explain the geometrical meaning of the basic…
One of the numerous results of the Theory of General Relativity is the appearance of Gravimagnetism, described already by Thirring and Lense in 1918 [THI 18]. Its understanding normally remains reserved to specialists. This article presents…
Einstein's theory of general relativity (GR) provides the best available description of gravity. The recent detection of gravitational waves and the first picture of a black hole have provided spectacular confirmations of GR, as well as…
We present a brief review on the Raychaudhuri equations. Beginning with a summary of the essential features of the original article by Raychaudhuri and subsequent work of numerous authors, we move on to a discussion of the equations in the…
This paper presents relevant modern mathematical formulations for (classical) gauge field theories, namely, ordinary differential geometry, noncommutative geometry, and transitive Lie algebroids. They provide rigorous frameworks to describe…
This chapter provides a brief introduction to the Kerr spacetime and rotating black holes, touching on the most common coordinate representations of the spacetime metric and the key features of the geometry -- the presence of horizons and…
This note aims to offer a non-technical and self-contained introduction to gravitational algebras and their applications in the nonequilibrium physics of gravitational systems. We begin by presenting foundational concepts from operator…
Preliminary results on a canonical formulation of general relativity based on an analogy with the string model of elementary particles are presented. Rather than the metric components, the basic fields of the formalism are taken to be the…
We compare and contrast the different points of view of rotation in general relativity, put forward by Mach, Thirring and Lense, and Goedel. Our analysis relies on two tools: (i) the Sagnac effect which allows us to measure rotations of a…
These notes offer a basic introduction to the primary mathematical concepts of quantum physics, and their physical significance, from the operator and Hilbert space point of view, highlighting more what are essentially the abstract…
The paper constructs a generalized metrical multi-time Lagrange space, which allows a natural development of relativistic geometrical optics theories, in a general setting.
Extended Theories of Gravity can be considered a new paradigm to cure shortcomings of General Relativity at infrared and ultraviolet scales. They are an approach that, by preserving the undoubtedly positive results of Einstein's Theory, is…
In this article, we will review Noether's Theorems and their application in General Relativity. We will present Noether's Theorems in their original form and restate them as they are usually applied to physics. Some basic equations of…
This paper presents some ideas which might assist teachers incorporating special relativity into an introductory physics curriculum. One can define the proper-time/velocity pair, as well as the coordinate-time/velocity pair, of a traveler…
We try to lay down the foundations of a Newtonian theory where inertia and gravitational fields appear in a unified way aiming to reach a better understanding of the general relativistic theory. We also formulate a kind of equivalence…
This work is focused on the theory of Gravitoelectromagnetism (GEM). In the first part of this work we present a brief review of gravitoelectromagnetism, we locate and discuss all the problems which appear in this approach. We also try to…
We briefly review ideas about ``noncommutativity of space-time'' and approaches toward a corresponding theory of gravity.
This is a brief review where some basic elements of non-commutative geometry are given. The rules and ingredients that enter in the construction of the standard model and grand unification models in non-commutative geometry are summarized.…
This paper considers the possibility that abstract thinking and advanced synthesis skills might encourage extraterrestrial civilizations to accept communication with mankind on Earth. For this purpose, a notation not relying upon the use of…
In general relativity (GR), the metric tensor of spacetime is essential since it represents the gravitational potential. In other gauge theories (such as electromagnetism), the so-called premetric approach succeeds in separating the purely…