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Starts With A Bang

General Relativity Rules: Einstein Victorious In Unprecedented Gravitational Redshift Test

When a star passes close to a supermassive black hole, it enters a region where space is more severely curved, and hence the light emitted from it has a greater potential well to climb out of. The loss of energy results in a gravitational redshift, independent of and superimposed atop any doppler (velocity) redshifts we’d observe.(NICOLE R. FULLER / NSF)

A star orbiting past our galaxy’s supermassive black hole offered a chance to test relativity as never before.


The supermassive black hole at the center of the Milky Way is the most extreme astrophysical object located within a million light-years of Earth. With an estimated four million solar masses, it’s the largest black hole in our galaxy and second largest, behind Andromeda’s, in the entire Local Group. If your goal is to probe Einstein’s theory of General Relativity more stringently than ever before, the environment around this black hole is the best testing ground provided by nature.

Since 1995, a team of astronomers led by Andrea Ghez at UCLA has been studying the orbits of stars near the galactic center. As time has progressed, their observational tools and techniques have improved. In 2018, the closest orbiting star to our supermassive black hole, S0–2, made its closest approach, reaching 2.7% the speed of light. In a tremendous new result, Einstein’s theory has been confirmed as never before. Here’s how.

A map of star density in the Milky Way and surrounding sky, clearly showing the Milky Way, large and small Magellanic Clouds, and others. But measuring the stars of the Milky Way itself is challenging, as living within the Milky Way renders us unable to view all the stars and their motions inside. Light-blocking dust obscures our view of the stars in the galactic plane, particularly towards the galactic center. All told, the Milky Way contains some 200–400 billion stars over its disk-like extent, with the Sun located some 25,000 light-years from the center. (ESA/GAIA)

The galactic center itself is an extraordinarily difficult place to observe. Located 25,000 light-years away, observers on Earth have to look directly through the plane of the Milky Way in order to visually measure the central region of the galaxy, a task made enormously difficult by the presence of interstellar dust. This intervening material can been seen as dark bands strewn across the Milky Way, even with the naked eye.

However, these dust grains are of a finite size, and while visible light is easily absorbed by them, light of a longer wavelength can pass through that dust unimpeded. If we look in infrared light, suddenly our view of the galactic center opens up, and we can even see the individual stars moving around. When we examine the galactic center, we see that they all make an elliptical orbit around a single point that emits no light: our galaxy’s supermassive black hole.

Even though we’ve had large, ground-based telescopes with infrared instruments for decades, the sheer density of stars near the galactic center made resolving them an impossible tasks. It was only through the twin techniques of speckle interferometry and adaptive optics that the stars themselves began to be revealed.

The atmosphere itself introduces effects that distort the light reaching the optics of any telescope, from turbulent airflow to molecules that absorb or refract light to charged particles that affect light based on its polarization. By taking large numbers of very short exposures, the time-varying effects of turbulence can be greatly reduced, transforming a point source that appears to be a speckled mess back into a point source. The computer processing required to make this technique of speckle interferometry a reality was prohibitive throughout much of the 1970s and 80s, but was routine by the early 2000s.

When light comes in from a distant source and makes its way through the atmosphere to our ground-based telescopes, we’ll typically observe an image like the one you see at the left. However, through processing techniques like speckle interferometry or adaptive optics, we can reconstruct the known point source at left, greatly reducing the distortion and providing an astronomers with a template to un-distort the remainder of the image. (WIKIMEDIA COMMONS USER RNT20)

The second advance, in adaptive optics, brought us even farther. In principle, a telescope is only limited in resolution by the number of wavelengths of light that can fit across its primary mirror. Make your mirror twice as large, or your light wavelengths half the size, and you’ll double your resolution. This is a piece of cake in space, but with the atmosphere involved, distortion means that practically, you’ll never achieve that ideal resolution.

Adaptive optics changes all of that. By either splitting or making a copy of the incoming light, you can take one copy and delay it, while the other is used in conjunction with a known point source to calculate the effects of the atmosphere, and the mirror shape needed to un-distort that light. By then adapting the mirror to the proper shape necessary to restore the light to its pre-atmospheric effects, the other copy then strikes the adaptive mirror, producing a ground-based image with space-based quality.

This 2-panel shows observations of the Galactic Center with and without Adaptive Optics, illustrating the resolution gain. Adaptive optics corrects for the blurring effects of the Earth’s atmosphere. Using a bright star, we measure how a wavefront of light is distorted by the atmosphere and quickly adjust the shape of a deformable mirror to remove these distortions. This enables individual stars to be resolved and tracked over time, in the infrared, from the ground.(UCLA GALACTIC CENTER GROUP — W.M. KECK OBSERVATORY LASER TEAM)

These techniques have been around for decades, but they’ve seen significant improvements throughout the 21st century. Right alongside them, new instruments have been built to extract even more and higher-quality data out of the collected light.

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The Ghez group at UCLA was first able to image, resolve, and accurately identify the positions of faint, individual stars at the galactic center beginning in 1995. Initially, only a few stars were visible, but as time progressed, more and more stars became visible and trackable. As the Ghez group began to collect better data, they inferred the necessary mass required to create those orbits: a black hole of approximately 4 million solar masses. As an even greater boon, they started noticing that a few of the stars passed extremely close to the supermassive black hole, setting up an incredible opportunity.

The orbit of S0–2 (yellow) located near the Milky Way’s supermassive black hole was just used, based on 2018 data, to test Einstein’s Theory of General Relativity. Other stars, like S0–102 and S0–38, make close approaches to Sagittarius A*, but S0–2 is the closest. If there are any departures from Einstein’s predictions observed, these results will lead the way towards a new, more fundamental and accurate theory of gravity. (A. GHEZ / W.M. KECK OBSERVATORY / UCLA GALACTIC CENTER GROUP)

The closest star of all was one of the earliest ones discovered by the Ghez group when examining the galactic center: S0–2. (This is out of approximately 100 resolved stars in the galactic center, overall.) At its closest, S0–2 comes within just 18 billion kilometers of the event horizon of Sagittarius A*, which is only about twice the diameter of Neptune’s orbit around the Sun.

The first close approach of S0–2 to Sagittarius A* occurred in 2002, back when the technology was still rapidly improving. But with a mere 16 year orbit, astronomers already started planning for the next big event: in May of 2018. During closest approach, S0–2 would move at its most rapid speed: approximately 2.7% the speed of light. But what would be even more significant would be the effects of severely curved space around the black hole, which leads to a number of fascinating effects in General Relativity.

When a quantum of radiation leaves a gravitational field, its frequency must be redshifted to conserve energy; when it falls in, it must be blueshifted. Only if gravitation itself is linked to not only mass but energy, too, does this make sense. Gravitational redshift is one of the core predictions of Einstein’s General Relativity, but has never been tested directly in such a strong-field environment as our galactic center. (VLAD2I AND MAPOS / ENGLISH WIKIPEDIA)

Perhaps the biggest prediction that would be tested in this extreme environment is that of gravitational redshift: the idea that photons emitted from deep within a gravitational potential well will have to lose energy in order to escape from this region of significantly curved space. General Relativity makes very specific predictions, based on the curvature of space in a region where the matter is located, for how significantly the light emitted by an object should be systematically shifted towards longer wavelengths and lower energies.

At these very large speeds and with a specific orientation with respect to our line-of-sight, scientists would need to combine both special relativistic effects due to the star’s motion with the general relativistic effect of curved space in order to extract predictions for the redshift that they’d measure during the critical time.

When a star approaches and then reaches the periapsis of its orbit around a supermassive black hole, its gravitational redshift and its speed both increase. In addition, the purely relativistic effects of orbital precession should affect the motion of this star around the galactic center. Either effect, if measured robustly, would confirm/validate or refute/falsify General Relativity in this new observational regime. (NICOLE R. FULLER, NSF)

But gravitational redshift isn’t the only prediction of relativity that this close approach of S0–2 to Sagittarius A* will test. In addition, the fast-moving star moving through this severely curved space should receive a slight kick to its orbit.

Just as Mercury’s perihelion precesses around the Sun due to General Relativity, S0–2 should similarly precess around this supermassive black hole, except with a much larger effect. In Newtonian gravity, for instance, a mass like S0–2 should make a perfectly closed ellipse in its orbit around a black hole, whereas in Einstein’s gravity, there should be a measurable change in the shape of that ellipse after a close pass by the black hole.

Owing to the effects of both its high velocity (Special Relativity) and the curvature of space (General Relativity), a star passing close to a black hole should undergo a number of important effects, which will translate into physical observables like the redshifting of its light and a slight but significant alteration of its elliptical orbit. The close approach of S0–2 in May of 2018 was the best chance we’ve gotten to examine these relativistic effects and scrutinize Einstein’s predictions. (ESO/M. KORNMESSER)

Last year, the GRAVITY collaboration, using a new, state-of-the-art interferometer aboard the Very Large Telescope that was specialized for near-infrared observations, was able to measure an effect of gravitational redshift that was inconsistent with Newtonian dynamics alone. With subsequent, improved data, scientists hoped to not just disfavor Newton’s theory even farther in a relativistic regime, but to put Einstein to an entirely new, unprecedented test.

Well, the Ghez group has done it.

Double Lasers from KECK I and KECK II create an artificial laser guide star to better help the telescope focus on a particular location and account for the atmosphere’s properties, taking advantage of some of the most advanced adaptive optics systems and techinques in the world. (ETHAN TWEEDY PHOTOGRAPHY — ETHANTWEEDIE.COM)

In a culmination of an observational campaign that’s spanned the last 25 years, they added a series of measurements taken from March through September of 2018 to the existing data from 1995–2017, including the moment of closest approach in May of 2018. Their results, published today in Science, yield three brand new results.

The first was that the gravitational redshift of S0–2 was measured, and was found to be consistent with Einstein’s predictions within 1-sigma uncertainties, while Newton’s results were excluded at greater than 5-sigma significance. This is, on its own, a gold-standard confirmation of Einstein’s General Relativity in an entirely new regime.

But this also yields the most accurate determination for the mass of and the distance to Sagittarius A*: the black hole at the Milky Way’s center. The new estimates are as follows:

  • Mass = 3,946,000 solar masses, with an uncertainty of 1.3%, and
  • a distance of 7,946 parsecs (25,900 light-years), with an uncertainty of only 0.7%.

This is the most knowledge we’ve ever had about relativity, our galactic center, and stars that orbit in severely curved spaces.

The supermassive black hole at the center of our galaxy, Sagittarius A*, flares brightly in X-rays whenever matter is devoured. In longer wavelengths of light, from infrared to radio, we can see the individual stars in this innermost portion of the galaxy. Owing to the observations of the Ghez group, we now have a confirmation of Einstein’s General Relativity under extreme conditions, as well as the best-ever measurements of the mass of and distance to Sagittarius A*. (X-RAY: NASA/UMASS/D.WANG ET AL., IR: NASA/STSCI)

The most interesting part of this result is that it clearly demonstrates the purely General Relativistic effect of gravitational redshift. The observations of S0–2 showcase an exact agreement with Einstein’s predictions, within the measurement uncertainties. When Einstein first conceived of General Relativity, he did so conceptually: with the idea that acceleration and gravitation were indistinguishable to an observer.

With the validation of Einstein’s predictions for the orbit of this star around the galactic center’s black hole, scientists have affirmed the equivalence principle, thereby ruling out or constraining alternative theories of gravity that violate this cornerstone of Einsteinian gravity. Gravitational redshifts have never been measured in environments where gravity is this strong, marking another first and another victory for Einstein. Even in the strongest environment ever probed, the predictions of General Relativity have yet to lead us astray.


Starts With A Bang is now on Forbes, and republished on Medium thanks to our Patreon supporters. Ethan has authored two books, Beyond The Galaxy, and Treknology: The Science of Star Trek from Tricorders to Warp Drive.


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