Scientists have proposed a new way to describe black holes that could overcome a major limitation in one of Stephen Hawking’s most influential ideas. The research introduces an updated approach to black hole thermodynamics that works even when black holes are changing over time, potentially offering new insights into how they form, merge, and slowly evaporate.
Black holes are among the most extreme objects in the known universe. They squeeze enormous amounts of mass into an incredibly small region, creating gravity so intense that not even light can escape. To understand these cosmic objects, physicists rely on Einstein’s theory of general relativity and quantum mechanics.
In the early 1970s, Stephen Hawking and other researchers discovered surprising connections between the laws of thermodynamics, which describe familiar processes such as heating water on a stove, and the behavior of black holes.
“Hawking’s laws of black hole mechanics provided a satisfying connecting between extreme and ordinary physics and have been the paradigm for 50 years, but they have a serious limitation,” said Abhay Ashtekar, Atherton University Professor and Evan Pugh Professor of Physics Emeritus in the Eberly College of Science at Penn State and the leader of the research team. “They were formulated for black holes at equilibrium, or unchanging over time, but black holes are constantly changing, they form, merge and eventually evaporate. We wanted to find a way to overcome this limitation and extend the laws to black holes that are out of equilibrium.”
Ashtekar and his colleagues have now proposed a new method for determining a black hole’s entropy, a quantity that measures disorder and, according to the second law of thermodynamics, can never decrease. Their findings, published in Physical Review Letters and selected as an Editor’s Suggestion, introduce an entropy measure that is more closely connected to a black hole’s spin and energy. The researchers say this could improve scientists’ understanding of dynamic events such as black hole mergers and evaporation.
Why Hawking’s Framework Needed an Update
“The laws of black hole mechanics came directly from Einstein’s equations,” said Daniel E. Paraizo, a graduate student in physics at Penn State and an author of the paper. “Because you cannot see into a black hole, it seemed that there could be an infinite number of ways to make a black hole making their entropy infinite as well. They were also thought to only absorb energy and never radiate, so their temperature was zero.”
At first, those ideas made black holes appear incompatible with the familiar laws of thermodynamics because they seemed to have infinite entropy and no temperature. Hawking later changed that picture by using quantum mechanics to demonstrate that black holes can emit particles and energy.
“This changed the thinking about the thermodynamic properties black holes from a sort of mathematical concept described by equations, to being more of a physical reality,” Paraizo said. “This opened the door to finding analogies in black holes of entropy and temperature used in thermodynamics.”
Hawking proposed that the size of a black hole’s event horizon, the boundary beyond which even light cannot escape, is proportional to its entropy. He also showed that a black hole’s temperature depends on a combination of its mass and spin.
A Better Measure for Dynamic Black Holes
According to the researchers, the problem is that Hawking’s approach works only when a black hole is in equilibrium.
“There is a problem, though,” said Jonathan Shu, a graduate student in physics at Penn State and an author of the paper. “These analogies only really work for a black hole that is at equilibrium. In dynamic situations, event horizons can form and grow in what we call flat regions of space-time, where nothing is happening. This makes them teleological — their properties cannot be determined just by the local physics of the black hole but instead rely on prediction of events that may or may not happen in the future. Therefore, the area of event horizons cannot be a measure of the physical entropy of dynamical black holes. If we want to understand black holes that are growing, evaporating, and merging, we need a viable alternative.”
The team’s solution replaces the traditional event horizon with what physicists call a “dynamical horizon,” a concept that is already widely used in computer simulations of black holes. Unlike an event horizon, a dynamical horizon is defined by the black hole’s properties at a specific moment in time, avoiding the complications created by relying on future events.
“This allows us to extend the first and second laws of thermodynamics to black holes that are not at equilibrium, thereby overcoming the limitations of the paradigm that has been used for over half a century,” Ashtekar said. “We can apply these generalized laws to better understand evaporating black holes in quantum theory and black hole mergers, like those detected by the LIGO-Virgo-KAGRA collaboration using gravitational waves.”
The research was supported by the Penn State Atherton Professorship Program and the Penn State Eberly College of Science.