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Cosmology

Cosmology

LIGO gravitational-wave signal backs up Hawking’s area theorem

13 Jul 2021
Simulated image of two black holes colliding
Cosmic testbed A computer simulation of the black-hole collision that produced the first gravitational wave signal to be detected, GW150914. (Courtesy: Simulating eXtreme Spacetimes (SXS) project/LIGO)

Stephen Hawking’s 40-year-old theorem about the area of a black hole’s event horizon has been confirmed thanks to data from the first burst of gravitational waves detected by LIGO. Known as Hawking’s area theorem, it states that the entropy of a black hole should not decrease. Because a black hole’s entropy is proportional to the area of its event horizon, that means the event horizon area should not decrease if two black holes merge, as they did in the cosmic cataclysm that produced the gravitational-wave signal dubbed GW150914.

To test Hawking’s area theorem, astronomers led by Maximiliano Isi of the Massachusetts Institute of Technology (MIT) re-examined the GW150914 signal, which was picked up by LIGO’s detectors in 2015 and announced in February of the following year. These ripples in space-time developed when black holes of 36 and 29 solar masses merged to form a new black hole of about 62 solar masses, with the three remaining solar masses converted into gravitational-wave energy.

If Hawking’s area theorem holds, the event horizon area of the newly merged “daughter” black hole should not be less than the combined area of the event horizons of the two parent black holes. Instead, Isi explains, “The combined changes in black hole masses and spins should conspire to result in an area increase – or, strictly speaking, to prevent an area decrease.”

Putting Hawking to the test

Gravitational-wave signals from merging black holes display a distinct sequence. At first, the in-spiraling black holes produce gravitational waves that increase in frequency and amplitude. A “ring-down” period then follows immediately after the merger, when the daughter black hole is in a distorted state and produces gravitational-wave vibrations somewhat analogous to the sound waves from ringing a bell.

By analysing the in-spiral and ring-down phases of GW150914, Isi’s team calculated the area of the two black holes’ event horizons based on their masses and rates of spin. They found that the combined area of the parent black holes’ event horizons was approximately 235 000 km2, whereas the area of the daughter black hole’s event horizon was approximately 367 000 km2. The total area had indeed increased, proving Hawking’s theorem to 95% confidence.

Deviations into exotic physics

Gaurav Khanna, a physicist at the University of Rhode Island and the University of Massachusetts, US, who was not involved in the research, calls the MIT study a “truly impressive work” that offers “the clearest such result” that Hawking’s theorem is true. “It’s really cool when gravitational-wave data is able to help test fundamental theorems of black-hole physics,” Khanna says.

Isi’s team now plan to study more black-hole mergers, searching for deviations from the theorem that may offer clues to new kinds of object, or even new physics. “Theorists have come up with more or less plausible models that could result in mixed populations of compact objects that could resemble black holes,” Isi tells Physics World. As examples, he cites quark stars and gravastars, which are hypothetical alternatives to black holes that contain a gravity-repelling area of space that prevents further collapse. Such extreme forms of matter could, he says, “support very compact objects that look like black holes from afar but have other properties as you get close to where the event horizon would be”.

Isi also points out that Einstein’s general theory of relativity doesn’t mesh well with quantum physics, and may eventually need to be corrected. “If so, it is likely that black holes would have additional features beyond what we expect,” he says. “More precise measurements in the future might allow us to place interesting constraints on these models.”

The research is published in Physical Review Letters.

  • This article was amended on 14 July 2021 to correct Maximiliano Isi’s institutional affiliation; he did his PhD research at the California Institute of Technology but is now at MIT.
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