Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Space-Time Curvature and the General Theory of Relativity

Space-Time Curvature and the General Theory of Relativity

In 1905, Albert Einstein published his special theory of relativity. According to this theory, no matter in the universe can attain a speed greater than the speed of light in a vacuum, which thus serves as the speed limit of the universe.
This has been verified in many experiments. However, space and time are no longer absolute. Two observers moving relative to one another do not agree on the length of objects or the passage of time. The mechanics of objects based on Newton's laws of...

Differential Form of Maxwell's Equations

Differential Form of Maxwell's Equations

James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and...

Schwarzschild Radius and Event Horizon

Schwarzschild Radius and Event Horizon

No object with a finite mass can travel faster than the speed of light in a vacuum. This fact has an interesting consequence in the domain of extremely high gravitational fields.
The minimum speed required to launch a projectile from the surface of an object to which it is gravitationally bound so that it eventually escapes the object’s gravitational field is called the escape velocity. The escape velocity is independent of the mass of the object. Merging the idea of escape...

Euler's Equations of Motion

Euler's Equations of Motion

In fluid mechanics, shear stresses arise from viscosity, which represents a fluid's internal resistance to deformation. For low-viscosity fluids, like water, these stresses are minimal, simplifying flow analysis by allowing the fluid to be treated as inviscid, or frictionless. In an inviscid fluid, shear stresses are absent, leaving only normal stresses, which act perpendicularly to fluid elements. Notably, pressure — defined as the negative of the normal stress — remains uniform across...

Euler Equations of Motion

Euler Equations of Motion

Imagine a rigid body that is rotating at an angular velocity of ω within an inertial frame of reference. Along with this, picture a second rotating frame that is attached to the body itself. This frame moves along with the body and possesses an angular velocity of Ω. The total moment about the center of mass is calculated by adding the rate of change of angular momentum about the center of mass in relation to the rotating frame and the cross-product of the body's angular velocity...

Principle of Equivalence

Principle of Equivalence

According to Albert Einstein (1897-1955), free-falling and feeling weightless are intrinsically linked. If a person were in free-fall under gravity, for example, diving towards the Earth from an airplane, they would feel completely weightless. Similarly, a person descending in a lift may feel partially weightless. Broadly speaking, it is assumed that an object in a uniform gravitational field and an object undergoing constant acceleration in the absence of gravity are under the same...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

A comparative mathematical modeling study of phenotypic approaches to T cell activation.

Scientific reports·2025

Same author

Autophosphorylation and the Dynamics of the Activation of Lck.

Bulletin of mathematical biology·2021

Same author

Unbounded solutions of models for glycolysis.

Journal of mathematical biology·2021

Same author

The minimal model of Hahn for the Calvin cycle.

Mathematical biosciences and engineering : MBE·2019

Same author

Dynamics of the Selkov oscillator.

Mathematical biosciences·2018

Same author

Energy intake functions and energy budgets of ectotherms and endotherms derived from their ontogenetic growth in body mass and timing of sexual maturation.

Journal of theoretical biology·2018

Search research articles

Related Experiment Video

Updated: Mar 8, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Theorems on Existence and Global Dynamics for the Einstein Equations.

Alan D Rendall¹

¹Max-Planck-Institut für Gravitationsphysik, Am Mühlenberg 1, 14424 Golm, Brandenburg Germany.

Living Reviews in Relativity

|February 7, 2017

Summary

This summary is machine-generated.

This guide explores theorems on Einstein equations, focusing on solution existence and global dynamics. It highlights open questions and surveys the Cauchy problem, global results, and spacetime construction.

More Related Videos

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Published on: June 15, 2022

Related Experiment Videos

Last Updated: Mar 8, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Published on: June 15, 2022

Area of Science:

General Relativity
Mathematical Physics

Background:

The Einstein equations are central to understanding gravity and spacetime.
The Cauchy problem and global dynamics of solutions are critical areas of research.

Purpose of the Study:

To provide a comprehensive guide to theorems on the existence and global dynamics of solutions to the Einstein equations.
To identify and discuss open questions in the field.
To offer a survey of established results and new developments.

Main Methods:

Survey of the local-in-time Cauchy problem.
Discussion of global results for symmetric solutions.
Presentation of comparative results from Newtonian theory and special relativity.
Analysis of global results for small data.
Construction of spacetimes with prescribed singularity structure.

Main Results:

A survey of the well-understood local-in-time Cauchy problem.
Discussion of global results for solutions with various symmetries.
Presentation of comparative results from Newtonian theory and special relativity.
Treatment of global results for small data.
Results on constructing spacetimes with prescribed singularity structure.
A conjectural picture of the asymptotic behavior of general cosmological solutions.

Conclusions:

The article synthesizes current knowledge on Einstein equations' solutions.
It identifies key open questions, guiding future research.
It provides a foundation for understanding spacetime dynamics and cosmology.