Related papers: Lectures on General Theory of Relativity
These lecture notes on Generalised Parton Distributions aim at providing a general picture of the field on the theoretical and phenomenological sides to master and Ph.D. students. They go along with the lecture given at the Baryon…
Course material for mathematical methods of theoretical physics intended for an undergraduate audience.
CONTENTS: 1 Introduction 2 Analytic Manifolds and Analytic Continuation of Metrics 3 Walker's Spacetimes and their Maximal Extension 4 Global Structure of de Sitter and Reissner-Nordstr\"om-de Sitter Cosmos 4.1 Special Cases 4.2 Collapsing…
This is a review with the ambitious goal of covering the recent progress in: 1) universal relations (in general relativity and alternative theories of gravity), and 2) neutron star models in alternative theories. We also aim to be…
These lecture notes concern information-theoretic notions of entropy. They are intended for, and have been successfully taught to, undergraduate students interested inresearch careers. Besides basic notions of analysis related to…
We present 18 Introductory Lectures on K-Theory covering its basic three branches, namely topological, analytic (K-Homology) and Higher Algebraic K-Theory, 6 lectures on each branch. The skeleton of these notes was provided by the author's…
\noindent 1. Generalities\hfil\break 2. Lie groups and Lie algebras\hfil\break 3. The unitary groups\hfil\break 4. Representations of the SU(n) groups (and of their algebras)\hfil\break 5. The tensor method for unitary groups, and\hb the…
These notes give a concise introduction to General Relativity at the advanced undergraduate level, starting from the weak field limit and gravitational waves, then introducing curved manifolds and Riemannian geometry. The nonlinear…
We consider some of the epistemic benefits of exploring "theory space" in the context of modifications of general relativity with intended applications in cosmology. We show how studying modifications of general relativity can help in…
In this lecture note, we give a basic introduction to the rapidly developing concepts of generalized symmetries, from the perspectives of both high energy physics and condensed matter physics. In particular, we emphasize on the (invertible)…
This text aims to explain general relativity to geometers who have no knowledge about physics. Using handwritten notes by Michel Vaugon, we construct the bases of the theory.
Einstein's theory of General Relativity is one of the pillars of modern physics. For decades, the theory has been mainly tested in the weak field regime with experiments in the Solar System and observations of binary pulsars. Thanks to a…
This manuscript is a shorthand version of my talk given at Odessa Gamov School on Astronomy, Cosmology and Beyond (22-28 August 2011, Odessa, Ukraine). Within this note we very briefly review the main achievements, new results and open…
Two complementary and equally important approaches to relativistic physics are explained. One is the standard approach, and the other is based on a study of the flows of an underlying physical substratum. Previous results concerning the…
In the framework of the special theory of relativity, the relativistic theory of gravitation (RTG) is constructed. The energy-momentum tensor density of all the matter fields (including gravitational one) is treated as a source of the…
The paper is devoted to technology of math. education in Russia in special mathematical schools ("listkovaya systema"). This system has positive sides and most classes in Russian mathematical schools or circles almost always uses it.…
It is shown that the most important effects of special and general theory of relativity can be understood in a simple and straightforward way. The system of units in which the speed of light $c$ is the unit of velocity allows to cast all…
We discuss certain recent metric space methods and some of the possibilities these methods provide, with special focus on various generalizations of Lyapunov exponents originally appearing in the theory of dynamical systems and differential…
The purpose is to introduce in a clear and direct way the students of undergraduate courses in physics and/or astronomy to the subject of radiative transfer. A pedagogical revision is made in order to obtain the radiative transfer equation,…
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…