General Relativity

Albert Einstein finished his general theory of relativity in November 1915 and its influence has been profound, dramatically influencing the direction of physics, cosmology, and mathematics. His field equations of gravitation explained how matter curves spacetime, how this curvature tells matter how to move, and it gave scientists the mathematical tools to understand how space would evolve in time, leading to a deeper understanding of the universe’s early conditions and development.

There is an interesting connection between two of the best-studied nonlinear partial differential equations in physics: the equations of hydrodynamics and the field equations of gravity.

Let’s start with a brief review of hydrodynamics. At...

In recent decades, physicists and astronomers have discovered two beautiful Standard Models, one for the quantum world of extremely short distances, and one for the universe as a whole. Both models have had spectacular success...

In 1935, Albert Einstein and collaborators wrote two papers at the Institute for Advanced Study. One was on quantum mechanics [1] and the other was on black holes [2]. The paper on quantum mechanics is very famous and influential. It pointed out...

In the public lecture “The Latest News from the Cosmos,” Matias Zaldarriaga, Professor in the School of Natural Sciences, explores the most detailed map of the infant universe to date. Publicly released on March 21, 2013, the...

Following the discovery in July of a Higgs-like boson—an effort that took more than fifty years of experimental work and more than 10,000 scientists and engineers working on the Large Hadron Collider—Juan Maldacena and Nima Arkani-Hamed, two...

John Brockman, founder and proprietor of the Edge website, asks a question every New Year and invites the public to answer it. THE EDGE QUESTION 2012 was, “What is your favorite deep, elegant, or beautiful explanation?” He...

The ancients thought that space and time were preexisting entities on which motion happens. Of course, this is also our naive intuition. According to Einstein’s theory of general relativity, we know that this is not true. Space and time are dynamical objects whose shape is modified by the bodies that move in it.

In the twentieth century, mathematicians developed a deep theory of knots, which was revolutionized by the discovery of the Jones polynomial—a way to calculate a number for every knot—by Vaughan F. R. Jones in the early...

It has been said that the goals of modern mathematics are recon­struction and development.1 The unifying conjectures between number theory and representation theory that Robert Langlands, Professor Emeritus in the School of Mathematics...

Why is the expansion of the universe speeding up, instead of being slowed by the gravitational attraction of galaxies and dark matter? What is the history of the Milky Way galaxy and of the chemical elements in its stars? Why are the planetary...

One of the remarkable discoveries in astrophysics has been the recognition that the material we see and are familiar with, which makes up the earth, the sun, the stars, and everyday objects, such as a table, is only a small fraction of all of the...

“Everything here is fraught with danger and excitement,” says Nima ­Arkani-­Hamed, Professor in the School of Natural Sciences. With a broad sweep of his hand, he motions to the diagram he has drawn on the chalkboard in his office of the range of...