相关论文: Quo Vadis, Mathematical General Relativity?
The mathematical theory of gravitational lensing has revealed many generic and global properties. Beginning with multiple imaging, we review Morse-theoretic image counting formulas and lower bound results, and complex-algebraic upper bounds…
This article reviews some aspects in the current relationship between mathematical and numerical General Relativity. Focus is placed on the description of isolated systems, with a particular emphasis on recent developments in the study of…
After recalling the conceptual foundations and the basic structure of general relativity, we review some of its main modern developments (apart from cosmology) : (i) the post-Newtonian limit and weak-field tests in the solar system, (ii)…
In this article we summarize what is known about the initial-boundary value problem for general relativity and discuss present problems related to it.
Based on several recent developments in relativistic astrophysics and observational cosmology, this article discusses prospects of (1) theoretical structure of General Relativity (GR) in the new era and (2) submission of GR to new and…
We discuss the status and some perspectives of relativistic quantum physics.
Outstanding questions in the study of relativistic jets in their various astrophysical settings are discussed in the context of a general dynamical model.
This paper presents a brief but comprehensive introduction to certain mathematical techniques in General Relativity. Familiar mathematical procedures are investigated taking into account the complications of introducing a non trivial…
This thesis is devoted to the study of gravitational theories which can be seen as modifications or generalisations of General Relativity. The motivation for considering such theories, stemming from Cosmology, High Energy Physics and…
An overview is provided of the singularity theorems in cosmological contexts at a level suitable for advanced graduate students. The necessary background from tensor and causal geometry to understand the theorems is supplied, the…
We review selected recent results concerning the global structure of solutions of the vacuum Einstein equations. The topics covered include quasi-local mass, strong cosmic censorship, non-linear stability, new constructions of solutions of…
A brief outline of the history of the discrepancies within Newtonian mechanics at the end of the nineteenth century is given. The framework of general relativity is described briefly and the famous 'tests' of general relativity are…
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.
Possibility of gravitational repulsion in General Relativity is discussed and astronomical data in favor of cosmological acceleration are described. The problem of vacuum energy is emphasized and possible ways of its solution are indicated.…
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…
The intention of this article is to give a flavour of some global problems in General Relativity. We cover a variety of topics, some of them related to the fundamental concept of 'Cauchy hypersurfaces': (1) structure of globally hyperbolic…
We explore the possibility of replacing point set topology by higher category theory and topos theory as the foundation for quantum general relativity. We discuss the BC model and problems of its interpretation, and connect with the…
I briefly review the current status of quantum gravity. After giving some general motivations for the need of such a theory, I discuss the main approaches in quantizing general relativity: Covariant approaches (perturbation theory,…
We discuss the issue of motivating the analysis of higher order gravity theories and their cosmologies and introduce a rule which states that these theories may be considered as a vehicle for testing whether certain properties may be of…
An attempt is made of giving a self-contained (although incomplete) introduction to holomorphic ideas in general relativity, following work over the last thirty years by several authors. The main topics are complex manifolds, two-component…