Jump to ContentJump to Main Navigation

You are looking at 1-20 of 37 items

  • Keywords: Einstein equations x
Clear All Modify Search

View:

General Relativity and Einstein's Equations

Yvonne Choquet-Bruhat

in General Relativity and the Einstein Equations

Published in print:
2008
Published Online:
May 2009
ISBN:
9780199230723
eISBN:
9780191710872
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199230723.003.0003
Subject:
Mathematics, Applied Mathematics

This chapter begins with a discussion of Newton's gravity law. It then covers general relativity, observations and experiments, Einstein's equations, field sources, Lagrangians, fluid sources, ... More


Local Cauchy Problem

Yvonne Choquet-Bruhat

in General Relativity and the Einstein Equations

Published in print:
2008
Published Online:
May 2009
ISBN:
9780199230723
eISBN:
9780191710872
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199230723.003.0006
Subject:
Mathematics, Applied Mathematics

This chapter begins with a discussion of moving frame formulae. It then covers n + 1 splitting adapted to space slices, constraints and evolution, Hamiltonian and symplectic formulation, Cauchy ... More


Global Existence Theorems: Asymptotically Euclidean Data

Yvonne Choquet-Bruhat

in General Relativity and the Einstein Equations

Published in print:
2008
Published Online:
May 2009
ISBN:
9780199230723
eISBN:
9780191710872
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199230723.003.0015
Subject:
Mathematics, Applied Mathematics

This chapter shows how the Penrose transform can be used to prove global existence of solutions of various semilinear field equations. It outlines the foundation points of Friedrich's conformal ... More


Relativistic Kinetic Theory

Yvonne Choquet-Bruhat

in General Relativity and the Einstein Equations

Published in print:
2008
Published Online:
May 2009
ISBN:
9780199230723
eISBN:
9780191710872
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199230723.003.0010
Subject:
Mathematics, Applied Mathematics

This chapter presents the basic equations of the relativistic kinetic theory; it proves local existence theorems for Einstein equations coupled with kinetic matter. It then provides thermodynamic ... More


BRIEF REVIEW OF GENERAL RELATIVITY

Miguel Alcubierre

in Introduction to 3+1 Numerical Relativity

Published in print:
2008
Published Online:
September 2008
ISBN:
9780199205677
eISBN:
9780191709371
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199205677.003.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter presents some of the basic concepts of general relativity. Topics discussed include notation and conventions, special relativity, manifolds and tensors, the metric tensor, Lie ... More


GR as a geometric theory of gravity — II

Ta-Pei Cheng

in Relativity, Gravitation and Cosmology: A Basic Introduction

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199573639
eISBN:
9780191722448
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199573639.003.0014
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

The mathematical realization of equivalence principle (EP) is the principle of general covariance. General relativity (GR) equations must be covariant with respect to general coordinate ... More


5 GW generation by post-Newtonian sources

Michele Maggiore

in Gravitational Waves: Volume 1: Theory and Experiments

Published in print:
2007
Published Online:
January 2008
ISBN:
9780198570745
eISBN:
9780191717666
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570745.003.0005
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter discusses how to go beyond the limit of sources moving in flat space-time. For a self-gravitating system such as a binary star, assuming that space-time is flat means that its dynamics ... More


The Einstein‐Maxwell Equations, Extremal Kähler Metrics, and Seiberg‐Witten Theory

Claude LeBrun

in The Many Facets of Geometry: A Tribute to Nigel Hitchin

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199534920
eISBN:
9780191716010
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199534920.003.0003
Subject:
Mathematics, Geometry / Topology

Nigel Hitchin has played a key role in the exploration of four-dimensional Riemannian geometry, and in particular has made foundational contributions to the theory of self-dual manifolds, ... More


THE 3+1 FORMALISM

Miguel Alcubierre

in Introduction to 3+1 Numerical Relativity

Published in print:
2008
Published Online:
September 2008
ISBN:
9780199205677
eISBN:
9780191709371
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199205677.003.0002
Subject:
Physics, Theoretical, Computational, and Statistical Physics

There are several different approaches to the problem of separating the Einstein field equations in a way that allows us to give certain initial data, and from there obtain the subsequent evolution ... More


Other Hyperbolic-Elliptic Well-Posed Systems

Yvonne Choquet-Bruhat

in General Relativity and the Einstein Equations

Published in print:
2008
Published Online:
May 2009
ISBN:
9780199230723
eISBN:
9780191710872
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199230723.003.0008
Subject:
Mathematics, Applied Mathematics

This chapter presents well-posed hyperbolic or hyperbolic-elliptic systems that lead to the same local existence andgeometric uniqueness theorems as the wave gauge choice. However, these different ... More


GR as a geometric theory of gravity – I

Ta-Pei Cheng

in Relativity, Gravitation and Cosmology: A Basic Introduction

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199573639
eISBN:
9780191722448
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199573639.003.0006
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

A geometric description of equivalence principle physics of gravitational time dilation is presented. In this geometric theory, the metric plays the role of relativistic gravitational potential. ... More


Stationary Spacetimes and Black Holes

Yvonne Choquet-Bruhat

in General Relativity and the Einstein Equations

Published in print:
2008
Published Online:
May 2009
ISBN:
9780199230723
eISBN:
9780191710872
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199230723.003.0014
Subject:
Mathematics, Applied Mathematics

This chapter presents the proofs of fundamental uniqueness theorems for complete stationary solutions of the vacuum, or electrovac, solutions of the Einstein equations. It studies the properties of ... More


Formulations of the Einstein–Euler Equations

Luciano Rezzolla and Olindo Zanotti

in Relativistic Hydrodynamics

Published in print:
2013
Published Online:
January 2014
ISBN:
9780198528906
eISBN:
9780191746505
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528906.003.0007
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter, which opens the second part of the book devoted to the numerical solution of the relativistic-hydrodynamics equations, presents in a concise, yet complete, way the several formulations ... More


Linearized theory and gravitational waves

Ta-Pei Cheng

in Relativity, Gravitation and Cosmology: A Basic Introduction

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199573639
eISBN:
9780191722448
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199573639.003.0015
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

In the weak-field limit Einstein's equation can be linearized and it takes on form of the familiar wave equation. Gravitational waves may be viewed as ripples of curvature propagating in a background ... More


Why quantum gravity?

Claus Kiefer

in Quantum Gravity: Third Edition

Published in print:
2012
Published Online:
May 2012
ISBN:
9780199585205
eISBN:
9780191739378
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199585205.003.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This introductory chapter presents the general motivations for constructing a quantum theory of gravity. The main argument is the conceptual incompleteness of present theoretical physics. The chapter ... More


Covariant approaches to quantum gravity

Claus Kiefer

in Quantum Gravity: Third Edition

Published in print:
2012
Published Online:
May 2012
ISBN:
9780199585205
eISBN:
9780191739378
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199585205.003.0002
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter introduces the important concept of the graviton. It discusses at some length linearized quantum gravity and its implications. A central role is played by path-integral quantization from ... More


INITIAL DATA

Miguel Alcubierre

in Introduction to 3+1 Numerical Relativity

Published in print:
2008
Published Online:
September 2008
ISBN:
9780199205677
eISBN:
9780191709371
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199205677.003.0003
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Only six out of ten Einstein field equations contain time derivatives and therefore represent the true evolution equations of the spacetime geometry. The remaining four equations are constraints that ... More


On the Bounded L2 Curvature Conjecture

Sergiu Klainerman

Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, and Stephen Wainger (eds)

in Advances in Analysis: The Legacy of Elias M. Stein

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691159416
eISBN:
9781400848935
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691159416.003.0010
Subject:
Mathematics, Numerical Analysis

This chapter deals with a fundamental application of new methods to a geometric quasilinear equation to settle an important conjecture in General Relativity. According to the bounded L² curvature ... More


General Relativity and the Schwarzschild Metric

David M. Wittman

in The Elements of Relativity

Published in print:
2018
Published Online:
August 2018
ISBN:
9780199658633
eISBN:
9780191863653
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199658633.003.0018
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

Previously, we saw that variations in the time part of the spacetime metric cause free particles to accelerate, thus unifying gravity and relativity; and that orbits trace those accelerations, which ... More


General Relativity

Nicholas Manton and Nicholas Mee

in The Physical World: An Inspirational Tour of Fundamental Physics

Published in print:
2017
Published Online:
July 2017
ISBN:
9780198795933
eISBN:
9780191837111
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198795933.003.0007
Subject:
Physics, Condensed Matter Physics / Materials

This chapter presents the physical motivation for general relativity, derives the Einstein field equation and gives concise derivations of the main results of the theory. It begins with the ... More


View: