# School of Natural Sciences

## The Odd Couple: Quasars and Black Holes

### by Scott Tremaine

*A cosmic detective story*

Black holes are among the strangest predictions of Einstein’s general theory of relativity: regions of spacetime in which gravity is so strong that nothing—not even light—can escape. More precisely, a black hole is a singularity in spacetime surrounded by an event horizon, a surface that acts as a perfect one-way membrane: matter and radiation can enter the event horizon, but, once inside, can never escape. Remarkably, an isolated, uncharged black hole is completely characterized by only two parameters: its mass, and its spin or angular momentum.

Laboratory study of a macroscopic black hole is impossible with current or foreseeable technology, so the only way to test these predictions of Einstein’s theory is to find black holes in the heavens. Not surprisingly, isolated black holes are difficult to see. Not only are they black, they are also very small: a black hole with the mass of the Sun is only a few kilometers in diameter (this statement is deliberately vague: because black holes bend space, notions of “distance” close to a black hole are not unique). However, the prospects for detecting black holes in gas-rich environments are much better. The gas close to the black hole normally takes the form of a rotating disk, called an accretion disk: rather than falling directly into the black hole, the orbiting gas gradually spirals in toward the event horizon as its orbital energy is transformed into heat, which warms the gas until it glows. By the time the inward-spiraling gas disappears behind the event horizon a vast amount of radiation has been emitted from every kilogram of accreted gas.

## General Relativity at 100: Celebrating Its History, Influence, and Enduring Mysteries

*An exploration of its continuing impact across physics, cosmology, and mathematics*

Albert Einstein finished his general theory of relativity in November 1915, and in the hundred years since, its influence has been profound, dramatically influencing the direction of physics, cosmology, and mathematics. The theory upended Isaac Newton’s model of gravitation as a force of attraction between two masses and instead proposed that gravity is felt as a result of the warping by matter of the universe’s four-dimensional spacetime. 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.

“The general theory of relativity is based on profound and elegant principles that connect the physics of motion and mass to the geometry of space and time,” said Robbert Dijkgraaf, Director of the Institute and Leon Levy Professor, who gave a lecture “100 Years of Relativity” in October, sponsored by the Friends of the Institute. “With Einstein’s equations, even the universe itself became an object of study. Only now, after a century of calculations and observations, the full power of this theory has become visible, from black holes and gravitational lenses to the practical use of GPS devices.”

To celebrate the centennial of Einstein’s general theory of relativity, the Institute held a special two-day conference November 5–6, cohosted with Princeton University and made possible with major support from IAS Trustee Eric Schmidt, Executive Chairman of Alphabet Inc., and his wife Wendy. The conference, General Relativity at 100, examined the history and influence of relativity and its continuing impact on cutting-edge research, from cosmology and quantum gravity, to black holes and mathematical relativity.

## Dating the Earth, the Sun, and the Stars

### by Timothy Brandt

*Might stellar rotation explain the variance of ages seen in star clusters?*

“How big” is almost always an easier question to answer than “how old.” Though we can measure the sizes of animals and plants easily enough, we can often only guess at their ages. The same was long true of the cosmos. The ancient Greeks Eratosthenes and Aristarchus measured the size of the Earth and Moon, but could not begin to understand how old they were. With space telescopes, we can now even measure the distances to stars thousands of light-years away using parallax, the same geometric technique proposed by Aristarchus, but no new technology can overcome the fundamental mismatch between the human lifespan and the timescales of the Earth, stars, and universe itself. Despite this, we now know the ages of the Earth and the universe to much better than 1 percent, and are beginning to date individual stars. Our ability to measure ages, to place ourselves in time as well as in space, stands as one of the greatest achievements of the last one hundred years.

## Has the Mystery of the Gamma Rays from the Galactic Center Been Solved?

### by Timothy Brandt

Five years ago, NASA’s Fermi Gamma-ray Space Telescope saw more gamma rays than expected from the area around the center of our galaxy. Many scientists suggest that the extra gamma rays could be from the annihilation of dark matter particles. This exotic interpretation, however, requires ruling out all other possible sources of the gamma rays. While working at IAS as Members in the School of Natural Sciences, Bence Kocsis and I have discovered an ideal candidate source.

## From Quantum Field Theory Esoterica to Wide and Continuing Implications

### by Stephen Adler

*Exploring the connection between anomalies and counting quark degrees of freedom*

The article by Wally Greenberg in the spring 2015 *Institute Letter* mentions the anomalous axial current triangle diagram and describes its connection with counting quark degrees of freedom. This derives from a calculation I did when a long-term Member at the Institute in 1968, so I thought it would be useful to describe in detail the work done by me and by Bill Bardeen at the Institute on axial-vector or chiral anomalies. At ﬁrst, this work was considered to be quantum ﬁeld theory esoterica, but it has turned out to have wide and continuing implications.

But ﬁrst, what is an axial-vector? A vector is a directed arrow. If you hold your right hand up to a mirror with the thumb pointing towards the mirror, you will see as the image a left hand with the thumb pointing towards you. This reversal of direction is characteristic of a *vector* under inversion of the coordinate axes (in this case, inversion of the axis perpendicular to the mirror). But another behavior is possible: a directed arrow that remains the same under inversion of the coordinate axes. Such a quantity is called an *axial-vector* or *pseudovector*. In the Maxwell equations for electromagnetism, electric ﬁelds behave as vectors and magnetic ﬁelds behave as axial-vectors under coordinate inversion, so this distinction has been around for many years.