Physicists extend black hole thermodynamics beyond steady systems
Penn State researchers propose an entropy measure for changing black holes, with possible uses in studying mergers, evaporation and gravitational waves.
By Priya Raghavan · Science Reporter
3 min read
Penn State physicists have proposed a way to apply thermodynamic laws to black holes that are changing, rather than only to idealized steady ones. The work matters because real black holes form, collide and may evaporate, while a major framework associated with Stephen Hawking was built for equilibrium cases.
The study, by Abhay Ashtekar, Daniel E. Paraizo and Jonathan Shu, was published in Physical Review Letters, according to Penn State. The paper, titled “Thermodynamics of Black Holes, Far from Equilibrium,” was selected as an Editor’s Suggestion, the university said.
Black holes pack large amounts of mass into regions where gravity is so strong that light cannot escape. Physicists describe them using Einstein’s general relativity and quantum mechanics, Penn State said.
In the early 1970s, Hawking and other researchers linked black hole behavior to thermodynamics, the branch of physics that describes heat, temperature and disorder. Ashtekar, an emeritus professor of physics at Penn State and leader of the research team, said those laws helped connect extreme astrophysics with ordinary physical processes, but were written for black holes that do not change with time.
Why the older framework was limited
Paraizo, a Penn State physics graduate student and co-author, said the original laws came from Einstein’s equations. Early thinking treated black holes as objects with zero temperature and potentially infinite entropy because nothing inside them could be observed and they appeared only to absorb energy, he said.
Hawking later used quantum mechanics to show that black holes can radiate particles and energy, Penn State said. That made thermodynamic ideas such as temperature and entropy more physically meaningful for black holes.
Under Hawking’s approach, the area of the event horizon — the boundary past which light cannot return — is tied to a black hole’s entropy. Penn State said Hawking also related a black hole’s temperature to its mass and spin.
The difficulty, according to the researchers, is that event horizons do not work well as a physical entropy measure for black holes that are growing, merging or evaporating. Shu, another Penn State physics graduate student and co-author, said event horizons can develop and expand in flat regions of space-time, making their properties depend on what may occur later rather than only on local conditions.
A shift to dynamical horizons
The Penn State team instead uses a “dynamical horizon,” a concept already used in computer simulations of black holes, the university said. Unlike an event horizon, a dynamical horizon is defined by the black hole’s properties at a given time.
The researchers say that shift allows them to define an entropy measure more closely tied to a black hole’s spin and energy. Penn State said the proposal extends the first and second laws of thermodynamics to black holes away from equilibrium.
The second law says entropy cannot decrease. In the new framework, the team says that principle can be applied to changing black holes without relying on event horizons whose definition depends on future developments.
Ashtekar said the generalized laws could help physicists study evaporating black holes in quantum theory and mergers like those observed through gravitational waves by the LIGO-Virgo-KAGRA collaboration. Penn State said the work may improve understanding of events in which black holes grow, combine and lose energy over time.
The research was supported by the Penn State Atherton Professorship Program and the Penn State Eberly College of Science, according to the university.
This story draws on original reporting from ScienceDaily.