Related papers: Mathematical relativity
This is a kind of introduction to some basic topics in analysis, some of which would be covered in standard graduate courses, and some not. However, an important difference is that not much in the way of prerequisites are needed, beyond…
This lecture note is intended to prepare early-year master's and PhD students in data science or a related discipline with foundational ideas in machine learning. It starts with basic ideas in modern machine learning with classification as…
We attempt to see how closely we can formally obtain the planetary and light path equations of General Relativity by employing certain operations on the familiar Newtonian equation. This article is intended neither as an alternative to nor…
We provide some guidance and examples to clear up common misconceptions about special relativity. These misconceptions often come from trying to express the truths of special relativity in Newtonian terms rather than in terms more natural…
The AstroCamp is an academic excellence program in the field of astronomy and physics for students in the last 3 years of pre-university education, which often includes a course (or a significant part thereof) on Relativity. After an…
These lectures on supersymmetry and extra dimensions are aimed at finishing undergraduate and beginning postgraduate students with a background in quantum field theory and group theory. Basic knowledge in general relativity might be…
We do not present any original or new material. This is a tutorial addressed to students who need to study the microscopic derivation of the quantum-mechanical master equation encountered in many practical physical situations.
We review cosmological relativity, a new special theory of relativity that was recently developed for cosmology, and discuss in detail some of its aspects.
This is a written version of a series of lectures aimed at undergraduate students in astrophysics/particle theory/particle experiment. We summarize the important progress made in recent years towards understanding high energy astrophysical…
Brief lecture notes for a course about random matrices given at the University of Cambridge.
This is a semipopular introduction to the Special and General Theory of Relativity, with special emphasis on the geometrical aspects of both theories and their physical implications.
Non-perturbative quantum general relativity provides a possible framework to analyze issues related to black hole thermodynamics from a fundamental perspective. A pedagogical account of the recent developments in this area is given. The…
The theory of measurement is employed to elucidate the physical basis of general relativity. For measurements involving phenomena with intrinsic length or time scales, such scales must in general be negligible compared to the (translational…
Gravity theories with non-minimally coupled scalar fields are used as characteristic examples in order to demonstrate the challenges, pitfalls and future perspectives of considering alternatives to general relativity. These lecture notes…
This article reports on an investigation of student understanding of the concept of time in special relativity. A series of research tasks are discussed that illustrate, step-by-step, how student reasoning of fundamental concepts of…
The present text is a collection of notes about differential geometry prepared to some extent as part of tutorials about topics and applications related to tensor calculus. They can be regarded as continuation to the previous notes on…
The purpose of these lecture notes is to describe the gravitational lens effects in different astrophysical contexts. These notes are voluntarily focused on the fundamental mechanisms and the basic concepts that are useful to describe these…
This paper is based on a series of talks given at the ESI program on 'Mathematical Perspectives of Gravitation Beyond the Vacuum Regime' in February 2022. It is meant to be an introduction to the field of relativistic elasticity for readers…
Lecture notes to a one-term course on operator algebras and their application in physics. Very brief and basic introduction to the subject of Banach- and C-star algebras complemented with their appearance in physics. The course is intended…
These lecture notes in the De Rham-Hodge theory are designed for a 1-semester undergraduate course (in mathematics, physics, engineering, chemistry or biology). This landmark theory of the 20th Century mathematics gives a rigorous…