Black hole reverberations suggest the cosmic beasts are as ‘bald’ as cue balls

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A simulation of the undulating black hole formed by the merger of two smaller black holes

Simulating eXtreme Spacetimes project

Three years ago, astrophysicists electrified the world when they detected gravitational waves—infinitesimal ripples in space itself—set off when two massive black holes swirled into each other and merged about 1.3 billion light-years away. The ability to detect gravitational waves opened a new window on the cosmos and since then, physicists have spotted a dozen more black hole mergers and one merger of two dense neutron stars. But physicists had yet to use such observations to test the properties of black holes themselves—until now.

A team of theoretical astrophysicists has used data from that first event—spotted by the twin instruments of the Laser Interferometer Gravitational-Wave Observatory (LIGO) in Hanford, Washington, and Livingston, Louisiana—to probe the final merged black hole. Deciphering its oscillations much as a pianist might think about a chord, they confirmed—albeit with modest precision—a prediction of Albert Einsteins theory of gravity called the no-hair theorem.

“Thats really beautiful, you really want to see this,” says Daniel Holz, an astrophysicist and LIGO team member at the University of Chicago in Illinois who was not involved in the analysis.

A black hole is the ultraintense gravitational field left behind when a sufficiently massive star collapses under its own weight to an infinitesimal point. Within a certain distance of the point, nothing can escape, not even light, so the black hole forms an inky sphere. It has a definite—and enormous—mass, and it may spin like a top—typically at a fair fraction of the speed of light.

Otherwise, a black hole must be featureless, or so says Einsteins theory of gravity, general relativity. According to the theory, information that falls into a black hole is lost. That means a black hole can retain no trace of how it formed, says Saul Teukolsky, a theoretical astrophysicist at Cornell University. That proscription is known as the no-hair theorem because famed American theorist John Archibald Wheeler quipped that it meant black holes were as indistinguishable as bald pates.

Testing the theorem is no easy matter. Astronomers have spotted isolated black holes, but they can’t see their surfaces, which are shrouded in hot gas. (It’s the temperature of this hot gas that reveals the presence of a black hole.) Observations of gravitational waves open a new way to test the theorem, however, because the violent merger of black holes produces a larger black hole that undulates like shaken Jell-O, radiating gravitational waves. Using the waves to measure the frequencies of those fleeting oscillations provides a way to test the no-hair theorem.

The key clues are hidden in so-called overtones, frequencies that are generally lower and die out faster than the main, longest lived one. But measuring them seemed an unobtainable goal, as researchers assumed theyd have to wait until the initial chaos of the ringing died down. At that point, the overtones would be undetectable to LIGO and its partner, the Virgo gravitational wave detector in Italy. However, last summer, Matthew Giesler, a graduate student at the California Institute of Technology in Pasadena, used simulations to show that the entire merger back to the instant of collision could be understood as the simple sum of the fundamental signal and overtones of the main mode. “That was a surprise to everybody,” Teukolsky says.

When Teukolsky, Giesler, and colleagues reanalyzed the signal from the first black hole merger, they found the first overtone, as they reported yesterday in Physical Review Letters. Its frequency and duration agree with the predictions of general relativity—and thus, support the no-hair theory. Specifically, they point to a mass and spin that match those from computer simulations of the entire event, based on general relativity, to within 10%. That concordance supports the notion, baked into general relativity, that these are the only parameters that characterize the final black hole. “Thats what I would call a true test of the no-hair theorem,” Teukolsky says.

Holz urges caution, however, noting that the evidence for the overtone isnt quite strong enough to claim a definitive observation. “Its very exciting, but to say that theyve shown that the no-hair theorem is correct? I wouldnt put it that way.” Ultimately, he says, the goal is to measure multiple modes and show that they relate to one another as general relativity predicts—or not. Such “black hole spectroscopy” may have to wait for the Laser Interferometer Space Antenna, a much more sensitive space-based gravitational wave detector that scientists hope to launch in the early 2030s, Holz says.

But Teukolsky says the analysis suggests black hole spectroscopy may be in reach sooner than that. Given improvements to the sensitivity of the LIGO detectors, he says, its possible that even one very powerful black hole merger could reveal multiple overtones. “We could even hope to see something thats twice close as the first merger.”

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