Related papers: A Lean and Mean Introduction to Modern General Rel…
In these notes we give an introductory unified treatment to the topics of special relativity, Lorentz transformations and the Lorentz group, Einstein velocitiy addition, and gyrogroups and gyrovector spaces. An effort has been made to…
An introduction to applied mathematics written for students in engineering and science. Focus is on a rigorous presentation that also builds understanding by discussion, analogy, and examples. Discussion of concepts involved in modeling…
Most recent approaches to bilingual dictionary induction find a linear alignment between the word vector spaces of two languages. We show that projecting the two languages onto a third, latent space, rather than directly onto each other,…
This work is originally a Cambridge Part III essay. Throughout the paper, some aspects of General Relativity in higher dimensions are reviewed. The work presented draws a path within the wide landscape of higher dimensional black holes…
Geometric mechanics is usually studied in applied mathematics and most introductory texts are hence aimed at a mathematically minded audience. The present note tries to provide the intuition of geometric mechanics and to show the relevance…
The definition of a reference frame in General Relativity is achieved through the construction of a congruence of time-like world-lines. In this framework, splitting techniques enable us to express physical phenomena in analogy with Special…
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…
Riemannian metric learning is an emerging field in machine learning, unlocking new ways to encode complex data structures beyond traditional distance metric learning. While classical approaches rely on global distances in Euclidean space,…
Affine variational principle for General Relativity, proposed in 1978 by one of us (J.K.), is a good remedy for the non-universal properties of the standard, metric formulation, arising when the matter Lagrangian depends upon the metric…
This survey article is an introduction to Diophantine Geometry at a basic undergraduate level. It focuses on Diophantine Equations and the qualitative description of their solutions rather than detailed proofs.
The following are expanded lecture notes for the course of eight one hour lectures given by the second author at the 2014 summer school Asymptotic Analysis in General Relativity held in Grenoble by the Institut Fourier. The first four…
The aim of this text is to extend the theory of generalized ordinary differential equations to the setting of metric spaces. We present existence and uniqueness theorems that significantly improve previous results even when restricted back…
Due to the effectiveness of using machine learning in physics, it has been widely received increased attention in the literature. However, the notion of applying physics in machine learning has not been given much awareness to. This work is…
In this lecture I build up the motivation for relativity and gravitation based on general principles and common sense considerations which should fall in the sphere of appreciation of a general reader. There is a novel way of looking at…
The high accuracy of modern space astrometry requires the use of General Relativity to model the propagation of stellar light through the gravitational field encountered from a source to a given observer inside the Solar System. In this…
The precision reached by current and forthcoming strong-lensing observations requires to accurately model various perturbations to the main deflector. Hitherto, theoretical models have been developed to account for either cosmological…
The paper discusses the optimal conguration of one or more ring lasers to be used for measuring the general relativistic effects of the rotation of the earth, as manifested on the surface of the planet. The analysis is focused on devices…
This work introduces a novel three-fold classification of reference frames in General Relativity, distinguishing between Idealised Reference Frames (IRFs), Dynamical Reference Frames (DRFs), and Real Reference Frames (RRFs). By defining a…
The physical consistency of the match of piecewise-$C^0$ metrics is discussed. The mathematical theory of gravitational discontinuity hypersurfaces is generalized to cover the match of regularly discontinuous metrics. The mean-value…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…