Universal Exponents Characterise Black Hole Phase Transitions in Low-Temperature Limits

Black holes, those enigmatic objects predicted by Einstein’s theory of general relativity, undergo phase transitions – akin to water changing from liquid to ice – under certain conditions. Shao-Wen Wei, Shan-Ping Wu, Yu-Peng Zhang, and colleagues at the Key Laboratory of Quantum Theory and Applications of MoE now demonstrate that these transitions exhibit surprisingly universal behaviour at very low temperatures. The team’s work reveals three specific mathematical values, or ‘exponents’, that consistently describe how black holes change state, irrespective of their charge or spin. This discovery is significant because it suggests fundamental, underlying principles govern black hole behaviour, offering a deeper understanding of gravity and the nature of these extreme cosmic objects, even when they are far from the point where phase transitions typically occur.
Black holes, once considered simple gravitational sinks, are now understood to possess surprisingly complex thermodynamic properties. Recent research investigates the behaviour of black holes at extremely low temperatures, revealing universal characteristics that could deepen our understanding of gravity and quantum effects. This work builds upon the established idea that black holes aren’t just defined by gravity, but also behave as thermodynamic systems, radiating energy and possessing temperature and entropy.

Researchers are particularly interested in the phase transitions black holes undergo – changes between a smaller, denser state and a larger, less dense one – mirroring the liquid-gas transitions observed in everyday fluids. The study focuses on whether the critical exponents governing these transitions remain consistent regardless of the black hole’s charge or spin. Researchers examine both charged and rotating (Kerr) Anti-de Sitter (AdS) black holes, building on previous work that has demonstrated the existence of phase transitions in these systems.

By analyzing the geometry around the black hole and deriving an expression for the Hawking temperature – the temperature emitted by a black hole – the team modeled these systems. They then determined the critical point, where phase transitions occur, by solving equations related to the black hole’s entropy and temperature. The results demonstrate that even far below the critical point, in the near-zero temperature region, black holes exhibit universal properties.

By analyzing the coexistence curve – which describes the boundary between different phases – and examining pressure and volume changes, researchers derived three universal exponents: 1, 2, and a value related to the dimension of spacetime. Further studies confirm that these exponents remain unchanged irrespective of the black hole’s charge and spin. This universality offers valuable insights into the behaviour near the event horizon of extremal black holes and may indicate the onset of quantum gravity effects.

This discovery is significant because it provides a pathway to explore quantum gravity – a long-sought theory that unifies general relativity with quantum mechanics. By identifying universal properties in the low-temperature limit, researchers can potentially simplify complex calculations and gain insights into the behaviour of gravity at the most extreme conditions. The findings suggest that the equations governing black hole thermodynamics remain valid even as temperatures approach absolute zero, offering a powerful tool for probing the fundamental nature of spacetime and the quantum realm.

Further research will likely explore how these exponents relate to other black hole systems and potentially reveal deeper connections between gravity, thermodynamics, and critical phenomena.