相关论文: Quo Vadis, Mathematical General Relativity?

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.

In this report, which is an extended version of that appearing in the Proceedings of GR16, I will give a summary of the main topics covered in Session A.3. on mathematical relativity at GR16, Durban. The summary is mainly based on extended…

This is a survey of Rational Homotopy Theory, intended for a Mathematical Physics readership.

This work is originally a Cambridge Part III essay. Throughout the paper, some aspects of General Relativity in higher dimensions are reviewed. The work presented draws a path within the wide landscape of higher dimensional black holes…

This chapter briefly discusses the fundamental properties of black holes in general relativity, the discovery of astrophysical black holes and their main astronomical observations, how X-ray and $\gamma$-ray facilities can study these…

These notes summarize basic concepts underlying numerical relativity and in particular the numerical modeling of black hole dynamics as a source of gravitational waves. Main topics are the 3+1 decomposition of general relativity, the…

This is a review of the aspirations and disappointments of the canonical quantization of geometry. I compare the two chief ways of looking at canonical gravity, geometrodynamics and connection dynamics. I capture as much of the classical…

Some formulas and speculations are presented relative to integrable systems and quantum mechanics.

Enforcing the periodicity hypothesis of the "old" formulation of Quantum Mechanics we show the possibility for a new scenario where Special Relativity and Quantum Mechanics are unified in a Deterministic Field Theory [arXiv:0903.3680]. A…

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…

In these lectures general relativity is outlined as the classical field theory of gravity, emphasizing physical phenomena rather than mathematical formalism. Dynamical solutions representing traveling waves as well as stationary fields like…

This brief note, written for non-specialists, aims at drawing an introductive overview of the multiverse issue.

The nature of gravity is fundamental to understand the scaffolding of the Universe and its evolution. Einstein's general theory of relativity has been scrutinized for over ninety five years and shown to describe accurately all phenomena…

An earlier paper [1] presented a gravity theory based on the optics of de Broglie waves rather than curved space-time. While the universe's geometry is flat, it agrees with the standard tests of general relativity. A second paper [2] showed…

This is a review article for The Review of Particle Physics 2006 (aka the Particle Data Book). It forms a compact review of knowledge of the cosmological parameters as at May 2006. Topics included are Parametrizing the Universe; Extensions…

We present a list of open questions in mathematical physics. After a historical introduction, a number of problems in a variety of different fields are discussed, with the intention of giving an overall impression of the current status of…

In this presentation, I will summarize the present status of the developments with a Universal Theory of Relativity \cite{smw-utr}. Some general challenges to be overcome will also be discussed.

This is Chapter 1 in the book General Relativity and Gravitation: A Centennial Perspective, Edited by Abhay Ashtekar (Editor in Chief), Beverly Berger, James Isenberg, Malcolm MacCallum. Publisher: Cambridge University Press (June, 2015).…

Content: 1. Introduction 2. Regge calculus and dynamical triangulations Simplicial manifolds and piecewise linear spaces - dual complex and volume elements - curvature and Regge action - topological invariants - quantum Regge calculus -…

I report on recent progress in the exciting field of Numerical Relativity, with special attention to black hole horizons.