Since September 14, 2015, when the Laser Interferometer Gravitational-Wave Observatory (LIGO) made the first-ever direct detection of gravitational waves, the observatory has been making history. Cornell astrophysicists Saul Teukolsky and Larry Kidder earned a share in the 2016 Special Breakthrough Prize in Fundamental Physics – a $3 million award – for their contributions to the project.
Now, on the 10th anniversary of LIGO’s first discovery, the LIGO-VIRGO-KAGRA team has announced a black hole merger similar to its first detection. However, thanks to a decade’s worth of technological advances improving the detector sensitivity, the signal is dramatically clearer, allowing unprecedented tests of General Relativity to be performed.
The research is described in “GW250114: testing Hawking’s area law and the Kerr nature of black holes,” published Sept. 10 in Physical Review Letters. Teukolsky is a co-author, along with over 1,200 members of the collaboration.
By analyzing the frequencies of gravitational waves emitted by the merger of the black holes, the team was able to provide the best observational evidence captured to date for what is known as the black hole area theorem. This idea was put forth by Stephen Hawking in 1971 and says that the total surface areas of black holes cannot decrease.
When black holes merge, their masses combine, increasing the surface area. But they also lose energy in the form of gravitational waves. Additionally, the merger can cause the combined black hole to increase its spin, which leads to it having a smaller area. The black hole area theorem states that despite these competing factors, the total surface area must grow in size.
Later in the 1970’s, Hawking and physicist Jacob Bekenstein concluded that a black hole's area is proportional to its entropy, or degree of disorder. The findings paved the way for later groundbreaking work in the field of quantum gravity, which attempts to unite two pillars of modern physics: general relativity and quantum physics.
“The incredible accomplishments of the experimentalists have reduced the instrument noise to such an extent that we can now confirm Hawking’s theorem almost perfectly,” said Teukolsky, who is the Hans A. Bethe Professor of Physics and Astrophysics, Emeritus, in Cornell’s College of Arts and Sciences. He is also the Robinson Professor of Theoretical Astrophysics at Caltech.
Before the merger, the black holes had a total surface area of 240,000 square kilometers (roughly the size of Oregon), while the final area was about 400,000 square kilometers (roughly the size of California), a clear increase.
This is the second test of the black hole area theorem. An initial test was performed in 2021 by Teukolsky, working with colleagues at CalTech and StonyBrook, using data from the first GW150914 signal. But because that data was not as clean, the results had a confidence level of only 95 percent as compared to the new data’s 99.999 percent.
The trickiest part of the analysis was to determine the final surface area of the merged black hole. The surface areas of pre-merger black holes can be more readily gleaned as the pair spiral together, roiling space-time and producing gravitational waves. But after the black holes merge, the signal is not as clearcut. During this so-called ringdown phase, the final black hole vibrates like a struck bell as it settles down to equilibrium.
The space-time distortions induced by gravitational waves are incredibly miniscule, 700 trillion times smaller than the width of a human hair.
In the new study, the researchers were able to precisely measure the details of the ringdown phase, which allowed them to calculate the mass and spin of the black hole, and subsequently determine its surface area. More precisely, they were able, for the first time, to confidently pick out two distinct gravitational-wave modes in the ringdown phase. The modes are like characteristic sounds a bell would make when struck; they have somewhat similar frequencies but die out at different rates, which makes them hard to identify. The improved data for GW250114 meant that the team could extract the modes, demonstrating that the black hole's ringdown occurred exactly as predicted by Einstein’s theory.
By coincidence, the theoretical predictions of the ringdown follow from work by Teukolsky in the 1970s while he was a graduate student.
“I never thought that theoretical work I was doing back then would ever have application in the real world,” said Teukolsky.
