Particular Timelike Flows in Global Lorentzian Geometry
Author:
Publisher:
Published: 2013
Total Pages: 159
ISBN-13:
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Causality-Violating Lorentzian Manifolds Admitting a Shear-Free Timelike Flow
Author: Matthias Plaue
Publisher: Logos Verlag Berlin GmbH
Published: 2012
Total Pages: 112
ISBN-13: 3832531866
DOWNLOAD EBOOKThe Godel spacetime is an important cosmological solution of Einstein's field equations of gravitation. Although it does not offer a viable description of the physical universe, it illustrates the theoretical possibility of time travel. This work investigates world models similar to the Godel spacetime with particular emphasis on relations between kinematical properties (shear, vorticity, acceleration, expansion) and causality violation, i.e., the formation of closed timelike curves.
Global Lorentzian Geometry
Author: John K. Beem
Publisher: Routledge
Published: 2017-09-29
Total Pages: 656
ISBN-13: 1351444719
DOWNLOAD EBOOKBridging the gap between modern differential geometry and the mathematical physics of general relativity, this text, in its second edition, includes new and expanded material on topics such as the instability of both geodesic completeness and geodesic incompleteness for general space-times, geodesic connectibility, the generic condition, the sectional curvature function in a neighbourhood of degenerate two-plane, and proof of the Lorentzian Splitting Theorem.;Five or more copies may be ordered by college or university stores at a special student price, available on request.
Geometric Flows and the Geometry of Space-time
Author: Vicente Cortés
Publisher: Springer
Published: 2018-12-05
Total Pages: 121
ISBN-13: 3030011267
DOWNLOAD EBOOKThis book consists of two lecture notes on geometric flow equations (O. Schnürer) and Lorentzian geometry - holonomy, spinors and Cauchy Problems (H. Baum and T. Leistner) written by leading experts in these fields. It grew out of the summer school “Geometric flows and the geometry of space-time” held in Hamburg (2016) and provides an excellent introduction for students of mathematics and theoretical physics to important themes of current research in global analysis, differential geometry and mathematical physics
Developments in Lorentzian Geometry
Author: Alma L. Albujer
Publisher: Springer Nature
Published: 2022-10-06
Total Pages: 323
ISBN-13: 3031053796
DOWNLOAD EBOOKThis proceedings volume gathers selected, revised papers presented at the X International Meeting on Lorentzian Geometry (GeLoCor 2021), virtually held at the University of Córdoba, Spain, on February 1-5, 2021. It includes surveys describing the state-of-the-art in specific areas, and a selection of the most relevant results presented at the conference. Taken together, the papers offer an invaluable introduction to key topics discussed at the conference and an overview of the main techniques in use today. This volume also gathers extended revisions of key studies in this field. Bringing new results and examples, these unique contributions offer new perspectives to the original problems and, in most cases, extend and reinforce the robustness of previous findings. Hosted every two years since 2001, the International Meeting on Lorentzian Geometry has become one of the main events bringing together the leading experts on Lorentzian geometry. In this volume, the reader will find studies on spatial and null hypersurfaces, low regularity in general relativity, conformal structures, Lorentz-Finsler spacetimes, and more. Given its scope, the book will be of interest to both young and experienced mathematicians and physicists whose research involves general relativity and semi-Riemannian geometry.
Lorentzian Geometry and Related Topics
Author: María A. Cañadas-Pinedo
Publisher: Springer
Published: 2018-03-06
Total Pages: 278
ISBN-13: 3319662902
DOWNLOAD EBOOKThis volume contains a collection of research papers and useful surveys by experts in the field which provide a representative picture of the current status of this fascinating area. Based on contributions from the VIII International Meeting on Lorentzian Geometry, held at the University of Málaga, Spain, this volume covers topics such as distinguished (maximal, trapped, null, spacelike, constant mean curvature, umbilical...) submanifolds, causal completion of spacetimes, stationary regions and horizons in spacetimes, solitons in semi-Riemannian manifolds, relation between Lorentzian and Finslerian geometries and the oscillator spacetime. In the last decades Lorentzian geometry has experienced a significant impulse, which has transformed it from just a mathematical tool for general relativity to a consolidated branch of differential geometry, interesting in and of itself. Nowadays, this field provides a framework where many different mathematical techniques arise with applications to multiple parts of mathematics and physics. This book is addressed to differential geometers, mathematical physicists and relativists, and graduate students interested in the field.
Recent Trends in Lorentzian Geometry
Author: Miguel Sánchez
Publisher: Springer Science & Business Media
Published: 2012-11-06
Total Pages: 357
ISBN-13: 1461448972
DOWNLOAD EBOOKTraditionally, Lorentzian geometry has been used as a necessary tool to understand general relativity, as well as to explore new genuine geometric behaviors, far from classical Riemannian techniques. Recent progress has attracted a renewed interest in this theory for many researchers: long-standing global open problems have been solved, outstanding Lorentzian spaces and groups have been classified, new applications to mathematical relativity and high energy physics have been found, and further connections with other geometries have been developed. Samples of these fresh trends are presented in this volume, based on contributions from the VI International Meeting on Lorentzian Geometry, held at the University of Granada, Spain, in September, 2011. Topics such as geodesics, maximal, trapped and constant mean curvature submanifolds, classifications of manifolds with relevant symmetries, relations between Lorentzian and Finslerian geometries, and applications to mathematical physics are included. This book will be suitable for a broad audience of differential geometers, mathematical physicists and relativists, and researchers in the field.
Mathematics of Gravitation: Lorentzian geometry and Einstein equations
Author:
Publisher:
Published: 1997
Total Pages: 250
ISBN-13:
DOWNLOAD EBOOKCollection of Papers on Geometry, Analysis and Mathematical Physics
Author: Daqian Li
Publisher: World Scientific
Published: 1997
Total Pages: 196
ISBN-13: 9789810230241
DOWNLOAD EBOOKThis volume is published in honor of Professor Gu Chaohao, a renowned mathematician and member of the Chinese Academy of Sciences, on the occasion of his 70th birthday and his 50th year of educational work. The subjects covered by this collection are closely related to differential geometry, partial differential equations and mathematical physics ? the major areas in which Professor Gu has received notable achievements. Many distinguished mathematicians all over the world contributed their papers to this collection. This collection also consists of ?Gu Chaohao and I? written by C N Yang, ?The academic career and accomplishment of Professor Gu Chaohao? by T T Li and ?List of publications of Professor Gu Chaohao?.
Semi-Riemannian Geometry With Applications to Relativity
Author: Barrett O'Neill
Publisher: Academic Press
Published: 1983-07-29
Total Pages: 483
ISBN-13: 0080570577
DOWNLOAD EBOOKThis book is an exposition of semi-Riemannian geometry (also called pseudo-Riemannian geometry)--the study of a smooth manifold furnished with a metric tensor of arbitrary signature. The principal special cases are Riemannian geometry, where the metric is positive definite, and Lorentz geometry. For many years these two geometries have developed almost independently: Riemannian geometry reformulated in coordinate-free fashion and directed toward global problems, Lorentz geometry in classical tensor notation devoted to general relativity. More recently, this divergence has been reversed as physicists, turning increasingly toward invariant methods, have produced results of compelling mathematical interest.
