LIGO’s 10th anniversary gift confirms Hawking’s theorem

It’s hard to believe, but it’s now been 10 full years since the twin Advanced LIGO detectors — in Hanford, WA and Livingston, LA — were completed and turned on for the first time. Just days after they began operations, they saw the first-ever directly detected gravitational wave: GW150914, which signified the merger of two black holes. From across the Universe, a black hole of 36 times the mass of the Sun merged with another of 29 times the Sun’s mass, producing a remnant black hole of just 62 solar masses, with the other 3 solar masses getting converted into gravitational radiation via Einstein’s E = mc².

When those emitted waves arrived in each of the twin LIGO detectors, they changed the length of LIGO’s incredibly long, precise laser arms by less than the width of a single proton. Yet the signal was strong enough, and LIGO was sensitive enough, that those black hole properties could all be reconstructed, with the fact that the signals from both detectors matched showing that it wasn’t noise, it wasn’t an injected signal, and it wasn’t a fluke. For the first time in history, we had detected gravitational waves.

It’s now 10 years after that spectacular September 2015 event, and LIGO has just recently spotted a similar event: GW250114, from January of 2025. Unlike the first event, there’s so much more to learn from this one, showcasing just how far gravitational wave astronomy, driven by these world-class detectors, has come in such a short time.

An animated look at how spacetime responds as a mass moves through it helps showcase exactly how, qualitatively, it isn’t merely a sheet of fabric. Instead, all of 3D space itself gets curved by the presence and properties of the matter and energy within the Universe. Space doesn’t “change shape” instantaneously, everywhere, but is rather limited by the speed at which gravity can propagate through it: at the speed of light. The theory of general relativity is relativistically invariant, as are quantum field theories, which means that even though different observers don’t agree on what they measure, all of their measurements are consistent when transformed correctly.

It’s incredible to recognize how incredible detecting a gravitational wave at all actually is. When masses move through curved space — and in particular, space that’s been heavily distorted by the presence of another heavy, nearby mass — they experience something known as a radiation reaction. This was first worked out for electrically charged particles in an electromagnetic field, but it happens in gravitation, too, in exactly the same fashion. The fact that a mass, which itself distorts the fabric of space, moves through a region of space where the curvature is changing leads to the spontaneous emission of radiation: in this case, gravitational radiation. Because energy is conserved, and gravitational radiation (also known as a gravitational wave) carries energy, this leads to the decay of the mutual orbits of these masses.

For two comparable masses like black holes, this can lead to gravitational waves distorting the fabric of space by large amounts, with the size of the ripples in space decreasing the farther away one moves from the source: the masses that generate these ripples. By the time the ripples from GW150914 arrived at Earth, the size of those ripples, which translates into a quantity known as the strain amplitude for a gravitational wave detector, was down to 10^-21, or one part in one sextillion. Remarkably, the advanced LIGO detectors were so sensitive that they could detect these tiny strain amplitudes, and not even “just barely,” but with an impressive signal-to-noise ratio of 26:1.

GW150914 was the first ever direct detection and proof of the existence of gravitational waves. The waveform, detected by both LIGO observatories, Hanford and Livingston, matched the predictions of general relativity for a gravitational wave emanating from the inward spiral and merger of a pair of black holes of around 36 and 29 solar masses and the subsequent “ringdown” of the single resulting black hole.

These black holes were kind of remarkable, in the sense that seeing merging black holes that were both this massive and also this close was an unlikely event, from a statistical perspective. That large-amplitude signal was fortuitous, as either a significantly smaller set of masses or a substantially greater distance to this merger would have led to a smaller strain amplitude, which would have been much more difficult — and, given LIGO’s initial capabilities, perhaps even impossible — to detect. It turned out we did get lucky with that very first detection, because it remained the signal with the largest strain amplitude ever seen for several years.

In those early days of Advanced LIGO, we only wound up seeing about one source per month of observing time, making it incredibly serendipitous to see one just days after turning the detectors on for the first time. But we wouldn’t have to rely on serendipity forever. The LIGO collaboration, thanks to outstanding planning, would periodically upgrade and refine their detector and its various components, increasing its sensitivity each time. Upgrades including:

• improvements to the vacuum systems within the laser cavities, leading to the world’s most perfect vacuum in history,
• cooling the mirrors to reduce noise with each reflection, while maximizing and enhancing the reflectivity of those mirrors,
• improving the observatory’s resistance to seismic noise, where the limit is now set by the fact that the Earth has ever-present tectonic plates,
• and squeezing the quantum states, in a frequency-dependent way, of the laser light that’s used to measure and detect the incoming gravitational waves.

Within LIGO’s vacuum chamber, laser light is now created in not only a squeezed fashion, but where quantum squeezing occurs in a frequency-dependent fashion. The squeezer is operational in this photo, as green laser light is being pumped through it.

Whereas LIGO was initially detecting about one gravitational wave event per month, improvements in both its sensitivity and its range have led to it now detecting events approximately ten times as frequently: about once every three days. A tenfold improvement in detection sensitivity, with the same basic infrastructure, is an unheard-of level of advancement in a scientific endeavor such as this. These incremental improvements, conducted during the downtime in between various data-taking runs, have enabled LIGO to increase its haul of merging black holes from that first event, seen in 2015, to hundreds of events as of 2025. In fact, during the first period of the fourth observing run (known as O4A), LIGO saw more gravitational wave events than from all previous observing runs combined.

Still, that first event, GW150914, still held the record for the largest strain amplitude ever seen even though all of these advances. In every gravitational wave event where two black holes merge, there are three separate phases to probe:

• the inspiral phase, where the masses get closer and closer due to orbital decay from the emission of gravitational waves,
• the merger phase, where black holes go from having two separate event horizons to having one unified horizon that enshrouds both objects,
• and the ringdown phase, where the now-merged black holes settle down into their final, equilibrium state.

Although it’s the inspiral phase that enables us to detect these binary black hole mergers, because there’s so much signal that builds up over many orbits, it’s the ringdown phase, or that post-merger phase, that enables us to probe some of the most important aspects of General Relativity itself.

This illustration maps out the various stages of a supermassive black hole merger, and the expected signals that scientists believe will emerge as the event unfolds. Once the two pre-merger black holes pass within the same event horizon, no further gravitational waves get emitted, save for the “ringdown” phase due to the changing shape of the post-merger event horizon. During the inspiral and merger phases, however, gravitational wave signals are the easiest to detect.

The key to understanding why the ringdown phase is so important is to recognize that, in Einstein’s General Relativity, there are only three factors that determine the equilibrium state, shape, and size of a black hole’s event horizon: mass, electric charge, and spin. For any isolated, stationary black hole, these three parameters determine all of the properties of a realistic black hole’s event horizon. If we ignore electric charge, which is expected to be negligible for most physically real black holes (because matter is, overall, electrically neutral), then we can look to Roy Kerr’s famed 1963 paper — where he detailed what’s now known as the Kerr metric — for the exact solution for a spinning, massive black hole in spacetime.

But a just-merged pair of black holes isn’t in this ideal, equilibrium state quite yet. It has to go from its initial configuration into that equilibrium state, and that’s what the ringdown phase actually is. When you measure and detect those tiny, post-merger spacetime ripples, you’re seeing how the black hole goes from that post-merger state to its equilibrium state, enabling you to confirm that these post-merger black holes do indeed evolve rapidly into that Kerr state. However, those ringdowns, if we can measure them well enough, can go a step farther: they can test the Hawking area theorem for black holes, which asserts that if you have two black holes that merge, the area of the final, post-merger black hole must be greater than or equal to the sum of the pre-merger black hole areas, individually.

Encoded on the surface of the black hole can be bits (or quantum bits, i.e., qubits) of information, proportional to the event horizon’s surface area. When two black holes merge, there is a theorem from Stephen Hawking, sometimes known as the second law of black hole mechanics, that states that the post-merger area must always be greater than or equal to the sum of the pre-merger areas, with strong implications for entropy and thermodynamics.

That theorem, devised by Stephen Hawking way back in 1971, has profound implications. Because black holes have entropies that are defined by their areas, the Hawking area theorem is an important manifestation of the second law of thermodynamics: the law that says that the entropy of any closed, isolated system can only increase, never decrease, over time. When two black holes merge, that ringdown signal can be used to determine the area of the post-merger event horizon. Although a range of area increases are allowed, the lower bound is an increase 0, and the upper bound is three times the initial area. Anything outside of that range would violate Hawking’s area theorem.

Back in 2021, a team of researchers attempted to test Hawking’s area theorem with the then-strongest signal yet detected by LIGO: GW150914. Our very first gravitational wave event of all was still, even years later, the strongest gravitational wave black hole-black hole merger signal we had yet seen, and yet they were only able to gather weak (two-sigma, or about 95% confidence) evidence supporting the area law. What they were seeing was consistent with General Relativity and our most vaunted theoretical predictions, but the data wasn’t quite good enough to confirm it with the needed degree of confidence.

The raw data (gray points) and the reconstructed inspiral, merger, and ringdown signals (red and blue curves) are shown for each of the twin LIGO detectors in Hanford, WA and Livingston, LA respectively. This data makes GW250114 the most exquisite strong-field test of General Relativity ever observed in nature.

That’s where the new gravitational wave event GW250114 comes into play. Physically, the event was very similar to the first gravitational wave event ever observed: two black holes, of around 30 solar mases each, inspiraled and merged together from around a billion light-years away. The gravitational waves showed up in the detector with a strain amplitude of around 10^-21: huge for gravitational waves, but tiny on an absolute scale. But, as the researchers from the key paper were quick to point out, “thanks to the LIGO detectors now operating near their design sensitivity, it registers at a signal-to-noise ratio of 80, as opposed to 26 for GW150914 a decade ago.”

That’s more than a factor of three in improvement of the signal strength over just 10 years, which enables a much more confident and robust extraction of the key parameters and properties associated with this merger. You can see evidence of this increased sensitivity in the event’s waveform, above, in which you can see how well the data matches each of the theoretical curves for the inspiral, merger, and ringdown portions of the merger event. You can also see, from the graph below, how improved the mass of the two merging objects is between the 2025 event (blue) compared to the 2015 event (gray). The improvement is entirely due to upgrades and improvements to LIGO’s sensitivity.

This comparison graph shows the black hole masses of GW150914 and GW250114, respectively. Although the masses and distances of the merging black holes were comparable, the confidence in narrowing down what the masses were, as shown from the gray and blue bumps, respectively, showcases just how significantly improved LIGO’s detectors are today versus ten years ago.

When two black holes coalesce and merge, they aren’t yet in that ideal, stable configuration that is the hallmark of a realistic black hole: a Kerr black hole for a rotating black hole, or a Schwarzschild black hole for the non-rotating case. (All observed black holes, thus far, are thought to be rotating.) That final phase of gravitational wave emission is known as the ringdown phase because of its similarity to what happened to a bell when it’s struck with a mallet, clapper, or a jacquemart. A struck bell will ring, and that ringing will create overtones: not just ringing at a single frequency, but at multiple frequencies, that all decay away over time.

That’s what the “ringdown” phase of a gravitational wave merger is like: just milliseconds after the two black holes merge, they begin exhibiting a “fundamental mode” of ringing, plus detectable overtones that are like resonant, higher frequency vibrations that are related to the fundamental mode. For GW250114, they were able to detect both the fundamental mode and the first overtone in the ringdown data, and having both of those enabled the researchers to perform a key test: is the post-merger remnant Kerr-like in nature? As you can see from the figure below, lifted from their paper, the observed gravitational wave spectrum (orange and green contours) are highly consistent with the Kerr spacetime (gray shaded region), which is precisely what theory predicts. The best-fit point, marked with a black X, lies exactly within the preferred region.

Is the post-merger black hole formed from the gravitational wave event GW250114 Kerr-like in nature? An assessment of the ringdown’s fundamental frequency plus the first overtone (green and orange) show that it is consistent with Kerr’s predictions (gray band), with the best-fit point (black X) falling exactly in line with predictions.

But then we come to Hawking’s area law, which is sometimes known as the second law of black hole mechanics: that the black hole horizon area cannot decrease in time. It declares that, for:

• any two black holes that spin in any fashion, a maximum of 50% of the initial energy can be gravitationally radiated away,
• and for two black holes that aren’t spinning at all, a maximum of 29% of the initial energy can be gravitationally radiated away.

As long as we aren’t creating matter or electromagnetic radiation out of nothing (i.e., via Hawking radiation), as long as the objects are actual black holes and not naked singularities, and as long as the laws of General Relativity describe the Universe, these conditions cannot be violated.

Therefore, if we can measure the area of the post-merger object, it serves as a test of those assumptions: if the area obeys the Hawking area law, then those assumptions remain valid; if not, it means one or more must be wrong. Unlike the Kerr nature of the remnant, which focused on the ringdown portion of the signal, the Hawking area law focuses on the pre-merger signal and the peak of the merger signal: comparing the pre-merger areas with the area at the time of the merger itself. As you can see from the graph below, the full signal (in green) agrees with both the Hawking area theorem (left-hand bound) and the law of energy conservation (right-hand bound), and in excellent agreement with the General Relativity prediction (central gray band).

This figure from the scientific paper investigating the gravitational wave signal GW250114 shows the constraints on the area of the post-merger black hole compared to the pre-merger black holes for the event, with the bounds set by the Hawking area theorem on the left and from energy conservation on the right. The green bump shows the data-driven viable results, with the narrow gray bar representing the General Relativity prediction.

This is remarkable for a variety of reasons. Prior to this gravitational wave event, we had only very weak confirmation of the Kerr nature of post-merger black holes, which you obtain from exquisite measurements of the ringdown phase. Prior to this gravitational wave event, we had only weak (2-sigma confidence) of Hawking’s area theorem for black hole mergers, which you obtain by comparing the pre-merger black hole signals with the remnant at the time of the merger. And prior to this gravitational wave event, the most stringent strong-field test we had of General Relativity was from the very first gravitational wave event ever observed: GW150914.

No longer, not to any of that. Thanks to the incredible series of upgrades conducted at LIGO over the past decade, and due to the fact that both LIGO detectors are fully operational, we were able to surpass all of those previous limits with a new event — GW250114 — that, physically, was no better than the original event. Our detectors and our technologies were what was improved, and that enabled us to:

• confirm the Kerr nature of the post-merger remnant from the ringdown phase,
• vastly improve our confidence in Hawking’s area theorem (to an impressive 4.4-sigma confidence),
• find black holes at more than 10 times the initial rate from LIGO’s early days,
• and to have a new record-holder for the most stringent strong-field test of Einstein’s General Relativity.

It adds even more fuel to the already overwhelming science case to not only maintain and continue operating both LIGO detectors, but to move forward with LIGO II and LISA as next-generation gravitational wave observatories. The proof is in the results, and the key in continuing to obtain them are the twin LIGO observatories themselves.