Artist’s impression of orbiting black holes about to merge. New research, led by Penn State physicists, shows that the size of the resulting merged black hole can be predicted using simple thermodynamics.
Credit
LIGO/Caltech/MIT/R. Hurt (IPAC)
When two black holes orbit each other, they eventually spiral inward and collide in one of the most violent phenomena in the universe. This event releases an immense burst of energy in the form of gravitational waves—ripples in the fabric of spacetime
While predicting the final mass and spin of the resulting new black hole (the “remnant”) has traditionally required massive supercomputers to solve Einstein’s complex equations of general relativity, a team of physicists led by Penn State has discovered a much simpler method.
Published in the journal Physical Review Letters, the study demonstrates that the final state of a black hole merger can be predicted using simple, everyday thermodynamics.
The problem with general relativity
When a merger concludes, the newly formed black hole vibrates intensely—a phenomenon physicists compare to a “struck bell.” As it rings, it radiates away excess energy via gravitational waves until it settles into a calm, stable state. This final state is defined entirely by just two macroscopic properties: its final mass and its spin (angular momentum).
To calculate these two numbers from the initial properties of the two orbiting black holes, scientists have historically relied on numerical relativity. This field utilises supercomputers to simulate every deterministic detail of the collision based on Einstein’s equations. While highly accurate, these calculations are computationally expensive and offer little conceptual insight into why the system stabilises the way it does.
The maximum entropy conjecture for black hole mergers
The Penn State research team bypassed the supercomputers by drawing a parallel to basic thermodynamics—the branch of physics that dictates the behaviour of gases, engines, and everyday systems.
In classical thermodynamics, if you mix two containers of hot gas, you do not need to track the microscopic collisions of every individual molecule to find the final temperature and pressure.
Instead, you use the concept of entropy, a fundamental measure of randomness or disorder in a system. Because nature naturally tends to drift toward states of higher disorder simply because there are more ways for a system to be messy than tidy, a mixed gas will automatically stabilise at the point that maximises its total entropy.
The physicists extended this exact logic to binary black holes, creating the Maximum Entropy Conjecture for Black Hole Mergers:
Accounting for losses:
The team tracked the total mass (energy) and angular momentum (rotational motion) carried away from the system by the radiating gravitational waves.
The remnant sequence:
They mapped the remaining mass and spin onto a hypothetical sequence of rotating black hole models.
Maximising chaos:
They discovered that the entropy of this hypothetical sequence peaked at a specific point. Remarkably, this point of maximum entropy matched the actual mass and spin of the final remnant calculated by supercomputers to within a few per cent.
Bridging the gap between gases and gravity
Historically, black holes were thought to lie entirely outside the laws of thermodynamics until Stephen Hawking demonstrated in the 1970s that they could theoretically radiate energy. However, Hawking’s original formulation had limitations when applied to highly dynamic, violent events where black holes are actively forming, colliding, and reshaping spacetime.
The new Penn State framework overcomes these limitations. It suggests that a colliding black hole “forgets” the chaotic, step-by-step history of its violent merger because it is bound by the same fundamental organising principle that makes a room messy or mixes two gases: the universal drive to maximise entropy.
Looking beyond the merger
By proving that thermodynamic principles apply with such precision to the universe’s most extreme gravitational events, the study raises a deeper philosophical and practical question for theoretical physics.
Rather than treating general relativity and thermodynamics as entirely separate frameworks, the team’s success raises the possibility that entropy maximisation is a fundamental organising law governing all black hole interactions across the cosmos.
This could dramatically streamline the way scientists interpret gravitational-wave data detected on Earth, allowing them to decode deep-space collisions without continuously relying on supercomputer simulations.