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The quantum superposition of two microstates with a black hole corresponds to that of another microstate. Credit: Aruna Balasubramanian

Black holes are intriguing astronomical objects with a gravity so strong that any object and even light cannot escape. Although black holes have been the subject of countless astrophysical studies, their origins and underlying physics remain largely a mystery.

Researchers from the University of Pennsylvania and the Centro Atómico Bariloche recently introduced a new model of black hole microstates, which investigates the origin of the entropy (i.e. the degree of disorder) in black holes.

This model, presented in an article published in *Physical Assessment Letters*provides an alternative perspective on black holes that could inform future astrophysics research.

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

‘According to statistical physics, as developed by Boltzmann and Gibbs in the late 19th 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 the quantum superpositions of ‘microstates’, that is, microscopic constituents that yield the same observable properties on a large scale.”

Physicists have been trying to provide a credible account of black hole entropy for decades. In the 1990s, Andrew Strominger and Cumrun Vafa took advantage of a hypothetical property known as ‘supersymmetry’ to devise a method to count the microstates of a special class of black holes for which the mass is equal to the electromagnetic charge, in universes with extra dimensions and multiple types of electric and magnetic fields.

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

“Despite previous attempts, there is no report yet that applies to the type of black holes created by stellar collapse in our world,” Balasubramanian said. “Our goal was to offer such an account.”

The main contribution of this recent work was the introduction of the new model of black hole microstates, which can be described in terms of collapsing dust envelopes within the black hole. Furthermore, the researchers devised a technique to count the ways in which these microstates can be superimposed quantum mechanically.

“The key insight of our work is that very different spacetime geometries corresponding to apparently different microstates can mix together due to the subtle effects of quantum mechanical ‘wormholes’ connecting distant regions of space,” Balasubramanian said.

“After taking into account the effects of these wormholes, our results showed that for any universe containing gravity and matter, the entropy of a black hole is directly proportional to the area of its event horizon, as Bekenstein and Hawking proposed.”

The recent work of Balasubramanian and his colleagues introduces a new way of thinking about black hole microstates. Their model describes them specifically as quantum superpositions of simple objects that are well described by classical physical theories of matter and spacetime geometry.

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

‘We also show that universes that differ from each other on a macroscopic, even cosmic scale, can sometimes be understood as quantum superpositions of other, macroscopically different universes. This is a manifestation of quantum mechanics on the scale of the entire universe, which is surprising. given that we generally associate quantum mechanics with small-scale phenomena.”

The newly introduced theoretical framework could pave the way for other theoretical work aimed at explaining black hole thermodynamics. In the meantime, the researchers plan to expand and enrich their description of black hole microstates.

“We are now studying to what extent and under what conditions an observer outside the event horizon can determine in which microstate a black hole is located,” says Balasubramanian.

**More information:**

Vijay Balasubramanian et al, Microscopic origins of the entropy of astrophysical black holes, *Physical Assessment Letters* (2024). DOI: 10.1103/PhysRevLett.132.141501

**Magazine information:**

Physical Assessment Letters

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