Related papers: A Lean and Mean Introduction to Modern General Rel…
At the University of Colorado Boulder, as part of our broader efforts to transform middle- and upper-division physics courses, we research students' difficulties with particular concepts, methods, and tools in classical mechanics,…
Upon straightforward four--directional extension of the special--relativistic two--dimensional transformations to the four--dimensional case we lead to convenient totally anisotropic kinematic transformations, which prove to reveal many…
The current paper deals with some new classes of Finsler metrics with reversible geodesics. We construct weighted quasi-metrics associated with these metrics. Further, we investigate some important geometric properties of weighted…
We present a way of teaching Einstein's special relativity. It starts with Galileo's relativity, the learners know from previous lectures. The lecture underlines that we can have three transformation equations for the space-time coordinates…
In a first course of general relativity it is usually quite difficult for students to grasp the concept of a geodesic. It is supposed to be straight (auto-parallel) and yet it 'looks' curved. In these situations it is very useful to have…
Introducing gravitational physics at high school provides educational means for bridging the gap between the image of science held by students and science itself. Natural language is fundamental in this learning. It engages students in…
General Relativity (GR) exists in different formulations. They are equivalent in pure gravity but generically lead to distinct predictions once matter is included. After a brief overview of various versions of GR, we focus on metric-affine…
The first part of these notes is a self-contained introduction to generalized complex geometry. It is intended as a `user manual' for tools used in the study of supersymmetric backgrounds of supergravity. In the second part we review some…
We develop a unifed theory to study geometry of manifolds with different holonomy groups. They are classified by (1) real, complex, quaternion or octonion number they are defined over and (2) being special or not. Specialty is an…
This is a substantially expanded version of a chapter-contribution to "The Springer Handbook of Spacetime", edited by Abhay Ashtekar and Vesselin Petkov, published by Springer Verlag in 2014. This contribution introduces the reader to the…
We present a study of the so called relaxed field equations of general relativity in terms of a decomposition of the metric; which is designed to deal with the notion of particles. Several known results are generalized to a coordinate free…
This paper aims to provide teachers with a tool to teach the essential features of special relativity, considering the students' difficulties highlighted by numerous studies. Our proposal presents special relativity as the solution to the…
The goal of this article is to present an introduction to loop quantum gravity -a background independent, non-perturbative approach to the problem of unification of general relativity and quantum physics, based on a quantum theory of…
We discuss the recent proposal of implementing Doubly Special Relativity in configuration space by means of Finsler geometry. Although this formalism leads to a consistent description of the dynamics of a particle, it does not seem to give…
In the Special Theory of Relativity space and time intervals are different in different frames of reference. As a consequence, the quantity 'velocity' of classical mechanics splits into different quantities in Special Relativity, coordinate…
This article is based on a talk given by the author at MSRI in the workshop "Connections for Women" in January 2013, while being a part of the program "Noncommutative Algebraic Geometry and Representation Theory" at MSRI. One purpose of the…
A partially alternative derivation of the expression for the time dilation effect in a uniform static gravitational field is obtained by means of a thought experiment in which rates of clocks at rest at different heights are compared using…
We study general relativity in the framework of non-commutative differential geometry. In particular, we introduce a gravity action for a space-time which is the product of a four dimensional manifold by a two-point space. In the simplest…
We give a standard introduction to loop quantum gravity, from the ADM variables to spin network states. We include a discussion on quantum geometry on a fixed graph and its relation to a discrete approximation of general relativity.
A variational principle is applied to 4D Euclidean space provided with a tensor refractive index, defining what can be seen as 4-dimensional optics (4DO). The geometry of such space is analysed, making no physical assumptions of any kind.…