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The quantum superposition of two microstates of a black hole is equivalent to a different microstate. Credit: Aruna Balasubramanian

Black holes are interesting astronomical objects that have such a strong gravity that they prevent any object, even light, from escaping. While black holes have been the subject of many astrophysical studies, their origins and fundamental physics remain largely a mystery.

Researchers at the University of Pennsylvania and the Bariloche Atomic Center recently presented a new model for black hole microstates regarding the origin of entropy (i.e., the degree of disorder) in black holes.

This model presented in A paper Published in *Physical review letters*It offers an alternative view on black holes that could benefit future astrophysical research.

“The Bekenstein-Hawking entropy formula, which describes the thermodynamics of black holes, was discovered in the 1970s,” Vijay Balasubramanian, a co-author of the paper, told Phys.org. “This formula indicates that black holes have an entropy proportional to the area of their horizons.

“According to statistical physics, as developed by Boltzmann and Gibbs in the late nineteenth century, the entropy of a system is related to the number of microscopic configurations that have the same macroscopic description.

“In a quantum mechanical world like ours, entropy arises from quantum superpositions of ‘microscopic states’, that is, microscopic components that produce the same observable features on large scales.”

Physicists have been trying to provide a reliable explanation for black hole entropy for decades. In the 1990s, Andrew Strominger and Cumron Vava took advantage of a hypothetical property known as “supersymmetry” to devise a way to calculate the exact states of a special class of black holes whose mass is equal to the electromagnetic charge, in extra-dimensional universes and multiple types of black holes. Electric and magnetic fields.

To explain the origin of the entropy of black holes in universes like ours, Balasubramanian and his colleagues had to create a new theoretical framework.

“Despite previous attempts, there is still no explanation that applies to the types of black holes that form as a result of stellar collapse in our universe,” Balasubramanian said. “Our goal was to provide such an account.”

The primary contribution of this recent work was the introduction of the new model of black hole microstates, which can be described in terms of the collapse of dust envelopes inside a black hole. In addition, the researchers have devised a technique to calculate the ways in which these quantum-mechanically precise states are superposed.

“The key idea of our work is that very different space-time geometries corresponding to apparently distinct microstates can blend into each other due to subtle effects of quantum mechanical ‘wormholes’ connecting distant regions of space,” Balasubramanian said.

“After accounting for the effects of these wormholes, our results show that for any universe containing gravity and matter, the entropy of a black hole is directly proportional to the area of the event horizon, as Bekenstein and Hawking suggested.”

Recent work by Balasubramanian and colleagues offers a new way of thinking about small states in a black hole. Their model specifically describes them as quantum superpositions of simple objects that are well described by classical physical theories of matter and the geometry of space-time.

“This is very surprising, because the community had expected that a microscopic explanation of entropy in black holes would require the full apparatus of a quantum theory of gravity, such as string theory,” Balasubramanian said.

“We have also shown that universes that differ from each other at the macroscopic, even cosmic, level can sometimes be understood as a quantum superposition of other universes that are different at the macroscopic level. This is a manifestation of quantum mechanics on the scale of the entire universe, which is surprising given that we usually “What we associate quantum mechanics with are small-scale phenomena.”

The newly presented theoretical framework could pave the way for other theoretical works aimed at explaining the thermodynamics of black holes. At the same time, the researchers plan to expand and enrich their description of small states in the black hole.

“We are now studying to what extent and under what conditions an observer outside the event horizon can determine the exact state in which the black hole exists,” Balasubramanian added.

**more information:**

Vijay Balasubramanian et al., The Microscopic Origin of Entropy of Astrophysical Black Holes, *Physical review letters* (2024). doi: 10.1103/PhysRevLett.132.141501

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