Dynamic black holes explained by simple thermodynamics?
New research led by Penn State scientists extends renowned physicist Stephen Hawking’s laws of black hole mechanics to dynamic black holes that form, merge and evaporate
Penn State
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Illustration of a black hole that is growing in response to an influx of energy. New research from Penn State suggests a new measure for a black hole’s entropy that extends Stephen Hawking’s laws of black hole mechanics to such out-of-equilibrium, dynamic black holes that form, merge and evaporate.
view moreCredit: Jonathan Shu and Daniel Paraizo, Penn State
UNIVERSITY PARK, Pa. — Of the known things in the universe, black holes are among the most extreme. They pack huge amounts of mass densely into a small area, producing gravity that is so strong that even light cannot escape. To describe their properties, physicists have relied on complex equations from Einstein’s theory of general relativity and quantum mechanics. But in the early 1970s, Stephen Hawking and other physicists found parallels between the thermodynamics laws describing ordinary things — like how a stovetop boils a pot of water — and black hole mechanics.
“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.”
Now, new research by Ashtekar and his team published and highlighted as an editor’s suggestion in the journal Physical Review Letters suggests an alternative way to determine a black hole’s entropy — a measure of disorder that can never decrease according to the second law of thermodynamics. The proposed new measure for entropy is more closely tied to the black hole’s physical properties of spin and energy and could open new doors for better understanding the dynamic processes black holes experience — from evaporation to merging with another black hole.
“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.”
With infinite entropy and zero temperature, black holes seemed beyond what thermodynamics could explain, but then Hawking used quantum mechanics to show that black holes can radiate energy and particles.
“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 suggested that the area of a black hole’s event horizon, the boundary around a black hole where gravity is still strong enough to prevent the escape of light, is proportional to its entropy and its temperature is inversely proportional to its a combination of its mass and spin.
“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 new research shows that event horizons can be replaced by so-called “dynamical horizons” that are already used in numerical simulations of black holes. The dynamical horizon is characterized using properties of the black hole at a given instant of time and is thus free from the problem of teleology.
“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.”
Funding from the Penn State Atherton Professorship Program and the Penn State Eberly College of Science supported the research.
Journal
Physical Review Letters
Subject of Research
Not applicable
Article Title
Thermodynamics of Black Holes, Far from Equilibrium
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