Study offers
evidence, based on gravitational waves, to show that the total area of a black
hole’s event horizon can never decrease.

There are
certain rules that even the most extreme objects in the universe must obey. A
central law for black holes predicts that the area of their event horizons —
the boundary beyond which nothing can ever escape — should never shrink. This
law is Hawking’s area theorem, named after physicist Stephen Hawking, who
derived the theorem in 1971.

Fifty years
later, physicists at MIT and elsewhere have now confirmed Hawking’s area
theorem for the first time, using observations of gravitational waves. Their
results appear today (July 1, 2021) in Physical Review Letters.

In the
study, the researchers take a closer look at GW150914, the first gravitational
wave signal detected by the Laser Interferometer Gravitational-wave Observatory
(LIGO), in 2015. The signal was a product of two inspiraling black holes that
generated a new black hole, along with a huge amount of energy that rippled
across space-time as gravitational waves.

If Hawking’s
area theorem holds, then the horizon area of the new black hole should not be
smaller than the total horizon area of its parent black holes. In the new
study, the physicists reanalyzed the signal from GW150914 before and after the
cosmic collision and found that indeed, the total event horizon area did not
decrease after the merger — a result that they report with 95 percent
confidence.

Physicists
at MIT and elsewhere have used gravitational waves to observationally confirm
Hawking’s black hole area theorem for the first time. This computer simulation
shows the collision of two black holes that produced the gravitational wave
signal, GW150914. Credit: Simulating eXtreme Spacetimes (SXS) project. Credit:
Courtesy of LIGO

Their
findings mark the first direct observational confirmation of Hawking’s area
theorem, which has been proven mathematically but never observed in nature
until now. The team plans to test future gravitational-wave signals to see if
they might further confirm Hawking’s theorem or be a sign of new, law-bending
physics.

“It is possible that there’s a zoo of different compact objects, and while some of them are the black holes that follow Einstein and Hawking’s laws, others may be slightly different beasts,” says lead author Maximiliano Isi, a NASA Einstein Postdoctoral Fellow in MIT’s Kavli Institute for Astrophysics and Space Research. “So, it’s not like you do this test once and it’s over. You do this once, and it’s the beginning.”

Isi’s
co-authors on the paper are Will Farr of Stony Brook University and the
Flatiron Institute’s Center for Computational Astrophysics, Matthew Giesler of
Cornell University, Mark Scheel of Caltech, and Saul Teukolsky of Cornell
University and Caltech.

**An age of
insights**

In 1971,
Stephen Hawking proposed the area theorem, which set off a series of
fundamental insights about black hole mechanics. The theorem predicts that the
total area of a black hole’s event horizon — and all black holes in the
universe, for that matter — should never decrease. The statement was a curious
parallel of the second law of thermodynamics, which states that the entropy, or
degree of disorder within an object, should also never decrease.

The
similarity between the two theories suggested that black holes could behave as
thermal, heat-emitting objects — a confounding proposition, as black holes by
their very nature were thought to never let energy escape, or radiate. Hawking
eventually squared the two ideas in 1974, showing that black holes could have
entropy and emit radiation over very long timescales if their quantum effects
were taken into account. This phenomenon was dubbed “Hawking radiation” and
remains one of the most fundamental revelations about black holes.

“It all started with Hawking’s realization that the total horizon area in black holes can never go down,” Isi says. “The area law encapsulates a golden age in the ’70s where all these insights were being produced.”

Hawking and
others have since shown that the area theorem works out mathematically, but
there had been no way to check it against nature until LIGO’s first detection
of gravitational waves.

Hawking, on
hearing of the result, quickly contacted LIGO co-founder Kip Thorne, the
Feynman Professor of Theoretical Physics at Caltech. His question: Could the
detection confirm the area theorem?

At the time,
researchers did not have the ability to pick out the necessary information
within the signal, before and after the merger, to determine whether the final
horizon area did not decrease, as Hawking’s theorem would assume. It wasn’t
until several years later, and the development of a technique by Isi and his
colleagues, when testing the area law became feasible.

**Before and
after**

In 2019, Isi
and his colleagues developed a technique to extract the reverberations
immediately following GW150914’s peak — the moment when the two parent black
holes collided to form a new black hole. The team used the technique to pick
out specific frequencies, or tones of the otherwise noisy aftermath, that they
could use to calculate the final black hole’s mass and spin.

A black
hole’s mass and spin are directly related to the area of its event horizon, and
Thorne, recalling Hawking’s query, approached them with a follow-up: Could they
use the same technique to compare the signal before and after the merger, and
confirm the area theorem?

The
researchers took on the challenge, and again split the GW150914 signal at its
peak. They developed a model to analyze the signal before the peak,
corresponding to the two inspiraling black holes, and to identify the mass and
spin of both black holes before they merged. From these estimates, they
calculated their total horizon areas — an estimate roughly equal to about
235,000 square kilometers, or roughly nine times the area of Massachusetts.

They then
used their previous technique to extract the “**ringdown,**” or reverberations of
the newly formed black hole, from which they calculated its mass and spin, and
ultimately its horizon area, which they found was equivalent to 367,000 square
kilometers (approximately 13 times the Bay State’s area).

“The data show with overwhelming confidence that the horizon area increased after the merger, and that the area law is satisfied with very high probability,” Isi says. “It was a relief that our result does agree with the paradigm that we expect, and does confirm our understanding of these complicated black hole mergers.”

The team
plans to further test Hawking’s area theorem, and other longstanding theories
of black hole mechanics, using data from LIGO and Virgo, its counterpart in
Italy.

“It’s encouraging that we can think in new, creative ways about gravitational-wave data, and reach questions we thought we couldn’t before,” Isi says. “We can keep teasing out pieces of information that speak directly to the pillars of what we think we understand. One day, this data may reveal something we didn’t expect.”

Reference: “Testing the Black-Hole Area Law with GW150914” by Maximiliano Isi, Will M. Farr, Matthew Giesler, Mark A. Scheel and Saul A. Teukolsky, 1 July 2021, Physical Review Letters. DOI:10.1103/PhysRevLett.127.011103

*This
research was supported, in part, by NASA, the Simons Foundation, and the
National Science Foundation.*