A new theoretical framework could extend Stephen Hawking’s famous laws of black-hole mechanics to the violent, constantly changing black holes found in the real universe.
Researchers at Penn State have proposed a new method for describing the thermodynamics of black holes while they are growing, merging or evaporating. Earlier formulations largely applied to idealised black holes in equilibrium—objects whose physical properties were assumed not to change over time.
The study, published in Physical Review Letters, was led by physicist Abhay Ashtekar with researchers Daniel E. Paraizo and Jonathan Shu. The paper was selected as an Editor’s Suggestion, highlighting its potential importance to gravitational physics.
The Connection Between Black Holes and Heat
During the early 1970s, Hawking and other physicists discovered that black holes appear to follow laws resembling ordinary thermodynamics.
Thermodynamics describes how heat, energy, temperature and entropy behave in physical systems. Entropy is often explained as a measure of disorder or of the number of possible internal arrangements a system can possess.
Black holes initially appeared incompatible with these familiar rules. Because nothing could escape them, physicists once assumed they absorbed energy without radiating it and therefore had a temperature of zero. Their hidden interiors also appeared capable of containing an enormous—or potentially unlimited—amount of information.
Hawking transformed that understanding by applying quantum mechanics to black holes. His work showed that black holes can emit particles and energy through what became known as Hawking radiation.
The discovery allowed physicists to associate black holes with temperature and entropy. In the traditional framework, the entropy of a black hole is related to the area of its event horizon—the boundary beyond which light and matter cannot return. Its temperature is connected to physical properties including mass and spin.
These relationships created an influential bridge between general relativity, quantum mechanics and thermodynamics. However, the Penn State researchers said the framework has a serious limitation: it works most naturally for black holes that have settled into equilibrium.
Real Black Holes Are Constantly Changing
Astrophysical black holes are rarely perfectly stable. They can absorb surrounding gas and stars, collide and merge with other black holes, or gradually lose energy through quantum processes.
These changing systems are described as being “far from equilibrium,” meaning their properties evolve over time.
The traditional event horizon becomes difficult to use in such situations because it is a global feature of space-time. Its precise location can depend not only on what is occurring around the black hole at a particular moment, but also on events that happen later.
Researchers describe this unusual feature as “teleological”. In theory, an event horizon can begin forming or expanding through an apparently quiet region because matter or energy will fall into the black hole in the future.
That creates a problem when physicists attempt to treat the event horizon’s area as a direct measure of a changing black hole’s physical entropy. A useful thermodynamic quantity should ideally be determined from the black hole’s condition at the moment it is being examined, rather than requiring knowledge of its future.
Dynamical Horizons Offer an Alternative
The Penn State team’s framework replaces the conventional event horizon with a “dynamical horizon”.
Dynamical horizons are already used in numerical simulations of evolving black holes. Unlike event horizons, they can be characterised using local physical information available at a particular moment.
The researchers developed an alternative entropy measure connected more directly to a changing black hole’s energy and spin.
According to the study, this approach allows versions of the first and second laws of thermodynamics to be applied to black holes outside equilibrium.
The first law relates changes in a system’s energy to other physical changes. For a black hole, these can include changes in its mass, rotation and horizon properties.
The second law states that total entropy does not decrease. In black-hole physics, an equivalent rule must explain how entropy behaves while a black hole absorbs material, changes shape or participates in a merger.
By using dynamical horizons, the researchers argue that these laws can be formulated without the future-dependent complications associated with event horizons.
Possible Applications to Black Hole Mergers
The framework could be particularly useful for studying black-hole mergers.
When two black holes spiral towards each other and collide, their masses, spins and surrounding geometry change rapidly. The event releases gravitational waves—distortions in space-time that can be detected by observatories on Earth.
Modern computer simulations already use dynamical horizons to follow black holes through these extreme events. A thermodynamic framework based on the same structures could help scientists interpret how energy, angular momentum and entropy evolve during a collision.
The researchers said the work may also contribute to theoretical studies of evaporating black holes. Hawking radiation suggests that black holes gradually lose mass and may eventually disappear, creating difficult questions about entropy and the fate of information that entered them.
A framework designed for evolving black holes could provide a more suitable basis for examining those questions than laws developed primarily for stationary systems.
A Theoretical Advance, Not a New Observation
The research does not report the discovery of a new black hole or a direct astronomical measurement. It presents a mathematical extension of black-hole thermodynamics.
Further work will be needed to explore how broadly the framework applies and how it connects with quantum theories of gravity, gravitational-wave modelling and the unresolved black-hole information problem.
It also does not overturn Hawking’s work. Instead, the researchers are attempting to preserve its central thermodynamic insights while expanding them to situations that the original equilibrium-based framework was not designed to describe.
Ashtekar said the generalised laws could provide a better way to study both quantum evaporation and black-hole mergers observed through gravitational waves.
The research was supported by Penn State’s Atherton Professorship Program and the university’s Eberly College of Science.
If the framework proves widely useful, it could offer physicists a more realistic thermodynamic description of black holes—not as perfectly settled objects, but as dynamic cosmic systems that continuously form, grow, collide and change.
