Understanding exact space-times

By Jiří Podolský 

---

General relativity is a unique gem, Einstein’s most brilliant idea, and his greatest gift to humankind. Conceived in 1915, it still remains the best theory of gravity. I’m sure Einstein himself would be surprised how remarkably well it describes reality, even in the most violent and dynamical situations. Just recall its recent spectacular vindication by the first direct detection of gravitational waves from binary black hole mergers at cosmological distances. What an achievement! Gravitational waves, black holes, cosmology – all three main ingredients and predictions of Einstein’s theory combined together.

Exact space-times

As we all know, Einstein’s equations determine the space-time geometry, which is the gravitational field. And we must take all their predictions seriously. Exact solutions to Einstein’s field equations include the mathematical truth about the physical reality. Unfortunately, it is often obscured, usually very deeply hidden. To dig out the physically measurable invariant quantities and consequences, is a painful mining process involving various techniques and methods. It is the real art of science.

It is essential to be well-equipped for the investigation of exact space-times. Nevertheless, here we are preparing to descend old silver mines in Kutná Hora, the source of great wealth of the Kingdom of Bohemia in the Middle Ages. (Jerry Griffiths and Jiří Podolský, April 2006)

A good month for Einstein – gravitational starlight deflection during the Great American Eclipse

by Dr. Donald G. Bruns

---

Don Bruns and his wife Carol on eclipse day at the Lions Camp on Casper Mtn. The tripod is bolted to the custom mosaic designed and built by his cousin Steve Lang.

After much anticipation, two experiments had great successes last year.  On August 17 2017, the LIGO/VIRGO collaboration monitored the merger of two neutron stars millions of light years away.  Only four days later in Wyoming, an experiment to measure the gravitational bending of starlight by the Sun acquired the best data since the idea was first tested in 1919, by Sir Arthur Eddington, in Africa.  I published my results on that experiment in Classical and Quantum Gravity on March 6, 2018.  My solo project to repeat Eddington’s achievement, which made Einstein famous, required a lot less manpower than LIGO!

Early last century, Einstein published his General Theory of Relativity that contained some unusual predictions, including the idea that massive bodies bend light beams.  The only way to test this would be during a total eclipse, when the sky would be dark enough to see stars close to the Sun, where the effect just might be measurable.

I started planning Eddington’s re-enactment when I found out that no one had attempted it since 1973 (also in Africa) and that no one had ever succeeded in getting all the parts to work during those precious few minutes of totality.  I assumed that with modern charge-coupled device (CCD) cameras and computerized telescopes, the experiment would be much easier.  I was wrong!  While some aspects were simplified (the Gaia star catalog provided accurate star positions, for example, and modern weather predictions and the compact equipment eased many logistics problems), dealing with pixels, turbulence, and a limited sensor dynamic range presented new challenges.

Some memories from meeting Einstein in 1951 – 1952

Yvonne Choquet-Bruhat is a French mathematician and physicist, renowned for her pioneering work on the initial value problem of General Relativity. Her work was one of the “Milestones of General Relativity” featured in a recent CQG focus issue. She has been on the faculty of the University of Marseille, the University of Reims and the University Pierre-et-Marie-Curie in Paris. She was the first woman to be elected to the French Academy of Sciences and is a Grand Croix of the Legion of Honour of France. She is also an elected member of the American Academy of Arts and Sciences. This reminiscence of Einstein was presented at the conference “A Century of General Relativity” held in Berlin, 30 November to 5 December, 2015. This image of Yvonne Choquet-Bruhat has been obtained from Wikipedia where it was made available by Momotaro under a CC-BY-SA 2.0 license. It is included within this article on that basis and attributed to Oberwolfach Photo Collection. 

I met Einstein in 1951 at the Institute for Advanced Study in Princeton. I was making there a postdoctoral stay, as assistant to the great mathematician Jean Leray, a part-time permanent professor at the IAS. I had defended a thesis on General Relativity under the official direction of André Lichnerowicz, but it was Jean Leray who had encouraged me to attack the problem of the existence of solutions of the Einstein equations taking given initial values, without assuming their analyticity. When I told Lichnerowicz about Leray’s suggestion, he said “it is too difficult for a beginner”. In fact it was not so difficult. In harmonic coordinates, called then “isotherm”, introduced by Lanczos, DeDonder and Georges Darmois, the Einstein equations in vacuum look like a system of quasidiagonal, quasilinear system of second order partial differential equations hyperbolic for a Lorentzian metric. I found by chance an article written in French by

General Relativity turns 100!

Clifford Will is the Editor-in-Chief of Classical and Quantum Gravity, Distinguished Professor of Physics at the University of Florida, Chercheur Associé at the Institut d’Astrophysique de Paris, and James McDonnell Professor of Space Sciences Emeritus at Washington University in St. Louis.

November 4, 1915 was a Thursday. It was the day that Albert Einstein gave the first of a series of four weekly lectures to the Prussian Academy of Sciences in Berlin. His life was a mess. He was separated from his wife Mileva, who had moved to Zurich taking his sons with her. He was having an affair with his second cousin Elsa. He was working night and day, was barely eating, and was suffering from stomach pains. He had agreed to give these lectures to present his theory of gravity but he still didn’t have it. To make matters worse, David Hilbert was racing to find the field equations first, and Einstein feared he would be beaten. Yet by the third lecture,