Does Einstein’s Theory of Gravity Hold Near Black Holes?

Scientists have been trying unsuccessfully to poke holes in Albert Einstein’s general theory of relativity for a full century. So far, however, Einstein’s theory has had it easy. Every assessment to date has been conducted in rather weak gravitational fields. To put general relativity to its greatest test, we need to see whether it holds up where gravity is extremely strong. And nowhere in the universe today is gravity stronger than at the edge of a black hole—at the event horizon, the boundary beyond which gravity is so overwhelming that light and matter that pass through can never escape.

The interior of a black hole is unobservable, but the gravitational field surrounding these objects causes matter close to the horizon to produce huge amounts of electromagnetic radiation that telescopes can detect. Near the black hole, the crushing force of gravity compresses inflowing matter, known as the accretion flow, into ever smaller volumes. This causes the infalling matter to reach temperatures of billions of degrees—which, ironically, makes the vicinity immediately surrounding a black hole one of the brightest spots in the cosmos.

If we could observe a black hole with a telescope with enough magnifying power to resolve the event horizon, we could follow matter as it spirals down toward the point of no return and see whether it behaves as general relativity says it should. There is, of course, a catch: developing a telescope that can resolve a black hole horizon poses several challenges. Notably we have to contend with the black hole’s tiny size when viewed from Earth. Even the supermassive black holes now thought to inhabit the centers of most galaxies, which weigh in at millions or billions of our sun’s mass and in some cases have diameters larger than our solar system, are so far away from Earth that they subtend incredibly tiny angles on the sky. The nearest example is Sagittarius A*, the four-million-solar-mass black hole at the center of the Milky Way; its event horizon would appear to be only 50 microarcseconds across, or roughly the size of a DVD seen on the moon. To resolve an object so small, a telescope must have an angular resolution more than 2,000 times finer than that achieved by the Hubble Space Telescope.

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What is more, such black holes are obscured from our view in two ways. First, they occur at the very centers of galaxies, deep within dense clouds of gas and dust that block most of the electromagnetic spectrum. Second, even material that emits the light we want to detect—that glowing whirlpool of crushed matter spiraling in toward the horizon—is itself opaque to most wavelengths of light. Consequently, there are only a few wavelengths of light that can escape from the black hole’s edge to be observed by us on Earth.

The Event Horizon Telescope (EHT) project is an international effort to overcome these hurdles and perform detailed observations of a black hole. To achieve the highest angular resolutions possible from the surface of Earth, the EHT exploits a technique known as very long baseline interferometry (VLBI), in which astronomers at radio dishes across the globe observe the same target simultaneously, record the data they collect on hard drives, and then later combine all those data using a supercomputer to form a single image. By doing so, many telescopes located on different continents can form one virtual Earth-sized telescope. The resolving power of a telescope is given by the ratio of the wavelength of light it observes to its size, and so VLBI routinely makes images of the radio sky with detail that far surpasses the magnifying power of any optical telescope.

By advancing the technologies used in VLBI so that observations can be made at the shortest radio wavelengths, the EHT will soon be able to meet all the challenges of black hole imaging. At these wavelengths (close to one millimeter in size), the Milky Way is largely transparent, enabling the EHT to observe Sagittarius A* with a minimum of blurring from the intervening gas. These same wavelengths are also able to pierce the matter falling toward the black hole, allowing access to the innermost regions surrounding Sagittarius A*’s event horizon. And in a true Goldilocks coincidence, the magnifying power of a globe-spanning VLBI array at millimeter wavelengths is well suited to resolving the event horizons of the nearest supermassive black holes.

In a parallel development, theoretical astrophysicists have developed mathematical models and computer simulations to explore a wide range of possible outcomes of these observations and to develop tools to interpret them. Using novel supercomputer algorithms, they have simulated the churn of matter just outside the black hole’s event horizon, and in all simulations they have found that the black hole casts a “shadow” on the light coming off the accretion flow.

University of Washington physicist James Bardeen predicted the existence of a black hole shadow in 1973. By definition, any light that crosses the event horizon can never return. Bardeen identified the point outside the horizon where a photon will orbit the black hole. If a light ray crosses this orbit heading inward, it is caught forever and spirals inward to the event horizon. Light rays originating between the event horizon and this orbit can escape, but they have to be pointed almost radially outward, or they, too, risk being caught by the black hole’s gravity and having their trajectories bent backward toward the event horizon. We call this boundary the photon orbit.

As far as light is concerned, the black hole acts like an opaque object, with the photon orbit defining its boundary. The contrast between the bright ring of the photon orbit and the dimmer interior is what is known as the shadow. The apparent size of this shadow as seen by observers on Earth is actually predicted to be quite a bit larger than the photon orbit. This occurs because the intense gravitational field surrounding the black hole “magnifies” the shadow through gravitational lensing.

The EHT is now poised to observe this shadow and other features of black holes. In 2007 and 2009 observations verified that the technological approach was sound—and that the ultimate science goal was within reach—by targeting Sagittarius A* and another supermassive black hole at the heart of the galaxy Virgo A (also known as M87). These early observations linked together sites in Hawaii, Arizona and California to successfully measure the extent of radio emission at a 1.3-millimeter wavelength from both sources. In both cases, the measurements matched the expected size of the black hole shadow.

Observations planned with the full, planet-spanning web of dishes will yield enough data to allow us to construct complete images of these black holes. An additional, equally important set of observations will use VLBI data to search for and trace the trajectories of localized active regions (“hotspots”) as they circle the black hole. Because general relativity predicts both what these black holes should look like and how matter should orbit them, these observations will allow us to perform a series of tests of Einstein’s theory of relativity in the place where its most extreme predictions become manifest.

Checking cosmic censorship

The EHT will enable us to answer a basic question: Is Sagittarius A* a black hole? All available evidence suggests that the answer is yes, but no one has ever directly observed a black hole, and other possibilities are consistent with general relativity. For example, Sagittarius A* could be something called a naked singularity.

A singularity in physics is a place where the solution to an equation is undefined and where the laws of nature as we understand them no longer operate. General relativity predicts that the universe began in a singularity—an initial moment when all the contents of the cosmos were concentrated into a single point of infinite density. The theory also tells us that a singularity, where gravity becomes infinite and matter is compressed to infinite density, lies at the center of every black hole.

In a black hole, the event horizon hides the singularity from our universe. General relativity does not require all singularities to be “clothed” by a horizon, however. There are an infinite number of solutions to Einstein’s equations in which the singularities are “naked.” Some of these solutions describe normal black holes spinning so fast that their horizons have “opened up” to reveal the singularity within; others describe black holes that have no event horizon.

Naked singularities, unlike black holes, remain highly theoretical: nobody has come up with a real-world recipe that would lead to their formation. Every astrophysically plausible computer simulation of the gravitational collapse of a star leads to the formation of a black hole with a horizon. Indeed, in 1969 Roger Penrose introduced the cosmic censorship hypothesis: the idea that physics somehow censors the nakedness of singularities by always enshrouding them with a horizon.

In September 1991 California Institute of Technology physicists John Preskill and Kip Thorne made a bet with University of Cambridge physicist Stephen Hawking that the cosmic censorship hypothesis is false and that naked singularities do exist. Even after Hawking’s death 27 years later the bet is still standing, begging for an experiment that will settle it. Proving that Sagittarius A* has an event horizon would not conclusively disprove the existence of naked singularities elsewhere. Yet determining that the black hole in the center of our Milky Way is a naked singularity would allow us to directly observe phenomena at conditions where modern physics breaks down.

Looking for hair

Discrediting cosmic censorship would not be a death blow to general relativity; after all, its equations allow for naked singularities. Yet we also expect the EHT to test a long-standing idea about black holes called the no-hair theorem. And if the no-hair theorem is false, general relativity will, at minimum, have to be modified; the mathematical proof of this theorem leaves no wiggle room.

The theorem says that any black hole that is surrounded by an event horizon can be completely described using just three properties: mass, spin and electrical charge. In other words, any two black holes with the same mass, spin and electrical charge are entirely identical, just as any two elecrons are indistinguishable. Black holes, the theorem states, have no “hair”—no geometric irregularities or distinguishing characteristics.

When we first started to think about imaging black holes using VLBI, we thought we could use the shapes and sizes of black hole shadows to learn the spins and orientations of the black holes that produced them. But our simulations presented us with an unexpected and, ultimately, very pleasant surprise. No matter how fast we let the black holes spin in our simulations, and no matter where we placed our mock observers, the black hole shadows always appeared nearly circular with an apparent size equal to about five times the radius of the event horizon. Because of some lucky coincidence—and if there is a deep physical reason for this, we still have not uncovered it—no matter how we alter the parameters in our models, the size and shape of the black hole shadow remain practically unchanged. This coincidence is excellent news if our goal is to test Einstein’s theory because it happens only if the general theory of relativity holds up [see box above]. If Sagittarius A* has an event horizon, and if the size or the shape of its shadow deviates from our predictions, that would constitute a violation of the no-hair theorem—and, thus, of general relativity.

Tracing orbits and more

EHT observations will generate a great deal more data than are used to make images. The antennas will record the full polarization of the radiation emitted by the black hole, which will enable us to create maps of the magnetic fields near the event horizon. Such maps could help us understand the physics behind the powerful “jets” emanating from the centers of galaxies such as M87—beams of extraordinarily energetic matter traveling near the speed of light for up to thousands of light-years. Astrophysicists believe that magnetic fields near the event horizon of supermassive black holes power these jets; mapping the magnetic fields could help us test that hypothesis.

We can learn other things by watching the motion of matter around a black hole. The accretion flows around the black holes are expected to be highly turbulent and variable. Computer simulations often show the presence of localized, short-lived, magnetically active regions in them—“hotspots” similar to magnetic eruptions on the surface of the sun. These hotspots, which may explain the brightness variations that are often seen in Sagittarius A*, would circle the black hole at nearly the speed of light, along with the underlying accretion flow, completing full orbits in less than half an hour. In some cases, they become gravitationally lensed as they move behind the black hole and generate nearly complete Einstein rings—bright, gravitationally warped circles of light just like those the Hubble Space Telescope has detected from distant quasars. In other cases, they orbit around the black hole a few times before they lose their energy and dissipate.

Hotspots could complicate the process of making an image because the VLBI technique uses telescopes much like a time-lapse camera, leaving the virtual shutter open for the full duration of the observation and using the natural rotation of Earth to get as many different angles on the black hole as possible. If a bright spot in the accretion flow orbits the black hole, its appearance will be smeared, just as a photograph of a sprinter will be blurry if the camera shutter is left open too long.

Yet hotspots could also enable us to perform an entirely different test of general relativity. The EHT can trace the orbits of hotspots using a technique that goes by the fancy name of closure phase variability tracking. The method involves measuring the delays between the time of arrival of light from the hotspot at three telescopes and then using basic triangulation to infer the position of the hotspot in the sky. Orbiting hotspots will produce distinctive signatures in the raw data collected by the telescopes. And in much the same way that Einstein’s equations predict the size and shape of the black hole shadow, they also disclose everything we need to know about the orbits that hotspots should trace. This hotspot model is somewhat schematic, and reality may be more complex. Nevertheless, at full sensitivity the EHT will be able to monitor structure in the accretion flow as it orbits the black hole, and that could provide yet another way of checking to see whether the predictions of general relativity hold up near the edge of a black hole.

Extraordinary evidence

What happens if our observations appear to disagree with Einstein’s theory? To use an expression popularized by Carl Sagan, extraordinary claims require extraordinary evidence. In the natural sciences, extraordinary evidence often means one or more verifications of any claim by independent methods. In the coming years, powerful optical and radio telescopes, as well as space-based gravitational-wave detectors, may provide such verification by monitoring the orbits of stars, neutron stars—tiny, incredibly dense objects produced by the gravitational collapse of massive stars—and other objects around supermassive black holes.

The Laser Interferometer Gravitational-wave Observatory (LIGO) detected gravitational waves from the coalescence of much smaller black holes than those found in the centers of galaxies, and as it will be accumulating more detections in the near future, it will help address whether these small black holes follow Einstein’s predictions. The optical interferometer GRAVITY on the European Southern Observatory’s Very Large Telescope (VLT) in Chile has tracked the orbits of stars in our galaxy that lie fairly close to Sagittarius A*’s event horizon—and found no evidence for unexpected phenomena at distances of about 1,000 times the radius of the black hole while continuing to push this limit closer to the event horizon itself. Once completed, the Square Kilometer Array (SKA), a radio interferometer under construction in South Africa and in Australia, will begin monitoring the orbits of rapidly spinning neutron stars, called pulsars, around the same black hole. Finally, the evolved Laser Interferometer Space Antenna (eLISA) will detect gravitational waves emitted as small compact objects orbit around supermassive black holes in nearby galaxies.

Because of the very strong gravitational fields of the black holes, the elliptical orbits of these objects will shift (precess) rapidly; this effect is so pronounced that the points of maximum distance from the black holes should trace a complete circle in only a few orbits. At the same time, the black holes will drag spacetime around with them, causing the orbital planes of objects within those spacetimes to precess as well. Measuring the rates of orbital precession for objects at different distances from a black hole will lead to a complete three-dimensional reconstruction of spacetime around a black hole, providing many tests of general relativity in the presence of extremely strong gravity.

Together all these instruments will help decide whether Einstein’s general theory of relativity—in particular, its predictions about black holes—will survive intact for another century or be sacrificed on the altar of scientific progress.