Related papers: A short course in general relativity
With the discovery of gravitational waves, the search for the quantum of gravity, the graviton, is imminent. We discuss the current status of the bounds on graviton mass from experiments as well as the theoretical understanding of these…
After a short review of prominent properties of gravitational waves and the newly born gravitational astronomy, we focus on theoretical aspects. Analytic approximation methods in general relativity have played a crucial role in the recent…
In the context of an extended General Relativity theory with boundary terms included, we introduce a new nonlinear quantum algebra involving a quantum differential operator, with the aim to calculate quantum geometric alterations when a…
Gravitational-wave sources offer us unique testbeds for probing strong-field, dynamical and nonlinear aspects of gravity. In this chapter, we give a brief overview of the current status and future prospects of testing General Relativity…
This work reports on the construction of a nonlinear distributional geometry (in the sense of Colombeau's special setting) and its applications to general relativity with a special focus on the distributional description of impulsive…
Introduction to the theoretical foundations of gravitational waves: from general relativity to detection and binary system waveforms. Lecture notes prepared for the MaNiTou summer school on gravitational waves. Draft chapter for the CNRS…
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…
General relativity describes gravitation in terms of the geometry of spacetime. It predicts the existence of gravitational waves (GWs) that stretch and compress spacetime and were detected recently by state-of-the-art interferometer…
General relativistic cosmology cannot be reduced to linear relativistic perturbations superposed on an isotropic and homogeneous (Friedmann-Robertson-Walker) background, even though such a simple scheme has been successfully applied to…
We provide a pedagogical approach to gravitational waves in cosmology with focus on gravitational wave signals related to primordial black holes. These lectures notes contain more details than one is able to present in the two two-hour…
This brief review is intended to introduce gravitational physicists to recent developments in which general relativity is being used to describe certain aspects of condensed matter systems, e.g., superconductivity.
These are expanded lecture notes of a mini-course whose objectives were to introduce the basic concepts, constructions and techniques of noncommutative geometry, as well as their uses as a framework for modelling quantum spacetime. Key…
The nascent field of gravitational-wave astronomy offers many opportunities for effective and inspirational astronomy outreach. Gravitational waves, the "ripples in space-time" predicted by Einstein's theory of General Relativity, are…
This Resource Letter provides some guidance on issues that arise in teaching general relativity at both the undergraduate and graduate levels. Particular emphasis is placed on strategies for presenting the mathematical material needed for…
This thesis contributes to the field of gravitational lensing (GL) and observational cosmology. We discuss the use of gravitational lensing as a tool in search of exotic objects in the Universe. In the next chapter the concordance of an…
The basic concepts of gravitational microlensing are introduced. We start with the lens equation, and then derive the image positions and magnifications. The statistical quantities of optical depth and event rate are then described. We…
Lecture notes written for a one-semester course in mathematical relativity aimed at mathematics and physics students. Not meant as an introduction to general relativity, but rather as a complementary, more advanced text.
Gravitational waves can act like gravitational lenses, affecting the observed positions, brightnesses, and redshifts of distant objects. Exact expressions for such effects are derived here in general relativity, allowing for…
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…
Towards the goal to quantize gravity, in this short review we discuss an intermediate step which consists in extending the picture of standard General Relativity by considering Extended Theories of Gravity. In this tapestry, the equations…