# Famous shadow of black hole provides novel test for new theories of gravity

Outwitting Albert Einstein just got even tougher. More than 100 years ago, the famous physicist published his explanation of gravity, known as general relativity (GR), which successfully explains everything from the orbits of planets to the bending of starlight. Still, some physicists have been trying to invent theories that can solve puzzles GR cannot—for example, by explaining away the need for invisible dark matter, whose gravity appears to bind the galaxies. But the first direct image of a black hole, revealed last year, has now provided a tough new test for theories of gravity. Fail it and your theory is dead.

“It’s a new hoop to jump through and a fairly narrow one,” says Feryal Özel, an astrophysicist at the University of Arizona who helped devise the new test.

In 1915, Einstein hypothesized that gravity arises because massive bodies like Earth warp space and time, or spacetime. That bent spacetime causes the path of a free-falling object to curve, resulting in the parabolic arc of a cannonball on Earth or the elliptical orbit of the Moon. In the 1930s, scientists discovered one surprising implication of GR: If a sufficiently massive star burns out, its core can collapse to an infinitesimal point, leaving behind nothing but a self-sustaining, ultraintense gravitational field—a black hole, so-called because within a certain distance, not even light can escape.

Only last year did humans get their first direct view of a black hole. This one was created not by a single collapsing star, but presumably formed when many black holes coalesced. It lurks in the heart of a galaxy 53 million light-years away and weighs 65 billion times as much as the Sun. To study it, a team of more than 180 astronomers and astrophysicists coordinated radio dishes around the globe to work as one big telescope in a project known as the Event Horizon Telescope (EHT).

The false-color image looks just like it ought to: a fiery ring surrounding an inky black dot. The glow emanates from hot gas that swirls around the black hole, and the dot in the middle is the “shadow” cast by the black hole as it captures any light that passes too close—even from the gas in front of it. EHT scientists used GR to calculate how big that shadow—which is also magnified by the black hole’s gravity—should appear, and found that their results agreed with the observation.

But they couldn’t use the image to test other theories of gravity, Özel explains, as they had no easy way to calculate how big the shadow should be if an alternative theory of gravity is at work. Now, Özel and colleagues have developed a fairly simple way to make that calculation, they report this week in Physical Review Letters. That’s no mean feat, as in principle there are almost innumerable ways that one might modify or expand on Einstein’s theory—say, by changing exactly how matter and energy warp spacetime. However, when used to describe a black hole, every theory eventually has to produce a metric—a mathematical expression that encodes the shape of the warped spacetime in the vicinity of the black hole.

That metric can be written in an approximate form as sum of ever smaller mathematical terms. The first term is well-known and gives the prediction of GR. Experiments in our own solar system have shown the next term—technically known as the first “post-Newtonian” correction—is very close to zero. Now, Özel and colleagues have shown that if they write out the math describing a black hole in the right way, the size of the shadow is determined by the next post-Newtonian correction. So to test a new theory of gravity, theorists need only to calculate the value it predicts for that second post-Newtonian parameter, Özel says. If the value falls outside a certain range, conflicting with the measured size of the shadow, the theory is out. Using the black hole’s shadow, the team has narrowed the possible range for the parameter by a factor of 500.

It’s surprising that a single parameter controls the size of the shadow, says Ilya Mandel, a theoretical astrophysicist at Monash University, Clayton. “I might have thought that there’s some combination of 23 parameters that determines the shadow’s size and that it’s going to be incredibly difficult to pull them apart,” he says.

But the test’s utility may be limited, says Emanuele Berti, a gravity theorist at Johns Hopkins University, as theorists don’t have many viable alternatives to GR to begin with. “Coming up with an alternative that is sufficiently different from GR to be tested while at the same time is compatible with the million things we already know about gravity is very hard,” he says.

More promising, researchers say, will be comparing the measurement of this particular parameter with measurements that can be teased out of another new source of information on gravity: the mergers of smaller black holes glimpsed via ripples in spacetime or gravitational waves. “Everybody who is doing a test of gravity is trying to put it in the same language [of post-Newtonian parameters] so that we can do this comparison,” says Lia Medeiros, an astrophysicist at the Institute for Advanced Study and author on the paper. If those measures differ, then GR might not be the final word on gravity.

***Correction, 2 October, 4:05 p.m.:** An earlier version of this story misspelled Lia Medeiros's name.