# New theory could reveal the microscopic nature of black holes

Studying black holes is key both to reconciling the theory of general relativity with quantum mechanics, and to gaining a deeper understanding of space and time at their extreme. However, it requires looking beyond the macroscopic features we can observe. The QUNAT (Quantum Mechanical Nature of Black Holes) project set out to do just that, with a new theory meant to lift the veil on black holes’ microscopic features.

In 1975, Benkenstein and Hawking came up with a formula to calculate black hole entropy, that is, the number of possible microscopic states consistent with the black hole’s observed macroscopic state. But this breakthrough also gave birth to one of the most significant outstanding problems in theoretical high energy physics: the information paradox of black holes. Although quantum theory tells us that information can’t get out of a black hole, this information is nowhere to be found, even in the radiations the black hole releases as it evaporates. A black hole can only be described by its mass, electric charge and angular momentum, and no information is encoded in it. In other words, there is currently no way to get a microscopic understanding of what a black hole is actually made of. ‘We can compare this situation to what we can see with water,’ says Troels Harmark, Professor of Theoretical Particle Physics and Cosmology at Niels Bohr Institute. ‘Water consists microscopically of water molecules (H20) which then again consist of other more elementary atoms and particles. But when we experience water we only see its macroscopic features such as its temperature and pressure. For black holes, these macroscopic features are quite well understood. We have their mass and temperature for instance. But we don’t understand very well their microscopic building blocks.’ Whilst significant progress has been made over the last decades, in particular for special classes of black holes in string theory, a full understanding that would encompass astrophysical black holes is still lacking. By finding a way to count all microscopic building blocks, Prof. Harmark aimed to reveal their entropy. His work under the QUNAT project picked up where the holographic principle – which resolves the black hole information paradox by assuming that black holes are two-dimensional surfaces projected in 3D – left off. ‘The idea of the holographic principle is that certain quantum theories without gravity, not living in our space-time, can describe the microscopic building blocks of black holes. These quantum theories live in fewer dimensions. This idea has all the right qualitative features to work,’ he explains. However, whilst few doubt the validity of the holographic principle, its workings are only completely understood in highly symmetric situations and when the strength of gravity is weak. Black holes and their extreme gravity are a whole other story: in order to truly understand their microscopic nature, the project team needed to take the coupling of their underlying quantum theory and increase it to be very large. To do that, they considered a limit of gravity and quantum mechanics where both of them simplify so much that it should be possible to take this large coupling limit. ‘In this limit, the black hole should be described with a new quantum mechanical theory that we discovered, called Spin Matrix Theory,’ Prof. Harmark explains. Thanks to this new theory, the team was notably able to understand the so-called D-branes – non-perturbative objects similar to black holes. They revealed how these D-branes, which are described classically in a gravitational background, emerge from a quantum theory, including their interactions. ‘This allowed for the first time for going beyond the supersymmetric limit of D-branes, since the interactions introduce non-supersymmetric corrections,’ says Prof. Harmark. Then, they could find the type of geometry that emerges from a concrete Spin Matrix theory. ‘Part of understanding black holes is to understand how geometry emerges from a quantum theory. In this case, we are able to understand the emergence of geometry from all Spin Matrix theories. This shows in particular that emergent geometry is a new type of geometry that has not been considered before.’ Prof. Niels Obers, deputy head of research at the Niels Bohr Institute and scientist in charge of the project, says these findings contribute to our understanding of how space and time emerge from an underlying quantum theory. ‘This could potentially be very useful for understanding the earliest part of the Big Bang where space and time emerge,’ he enthuses. Whilst the project is now completed, the team are continuing their work by studying the Spin Matrix theories that can be used to describe black holes, as well as pursuing the general idea that Spin Matrix Theory can provide new holographic correspondences that could help understand quantitatively how space and time emerge from a quantum theory.

## Keywords

QUNAT, black hole, microscopic features, general relativity, quantum mechanics, Hawking, Benkenstein, holographic principle, spin matrix theory, D-branes