Black holes turned out to be three-dimensional holograms

An international team of scientists has come to the conclusion that black holes can look like holograms, in which all the information they contain can be encoded on a two-dimensional surface. 

This model is consistent with Einstein’s theory of relativity, which describes black holes as three-dimensional, spherical, and smooth objects. An article by researchers is published in the journal Physical Review X.

It is known that black holes, within the framework of Einstein’s theory of relativity, have thermodynamic entropy, which, as discovered by Hawking, is proportional to the area of ​​the event horizon. In other words, the larger the black hole, the more information it carries in itself. Information, in this case, is the number of quantum microstates, as follows from quantum mechanics. However, both descriptions of black holes (quantum-mechanical and thermodynamic), as it turned out, conflict with each other.

To prove the correspondence between the two descriptions, experts applied a 30-year-old idea called the holographic principle of Hooft. It consists in the fact that all information contained in a certain region of a three-dimensional (or n-dimensional) space can be encoded on a two-dimensional boundary (or n-1-dimensional) surrounding this space. This helps to solve some fundamental physical problems, for example, describe the behavior of gravity in the region of the Universe in a system with fewer dimensions. In this case, there are no contradictions between quantum mechanics and Einstein’s theory of relativity, which physicists usually encounter when studying black holes.

The researchers described the properties of a black hole as a two-dimensional system in which gravity is not present explicitly, and accordingly, there is no contradiction generated by it. To do this, they applied a special kind of holographic principle called AdS / CFT matching. It consists in the fact that a certain five-dimensional space with negative curvature (anti-desitter space, AdS) is equivalent to a world-boundary with four dimensions. According to string theory, this boundary, called the brane, contains particles in the form of strings, and the behavior of these particles is similar to the behavior of particles in AdS with gravity.

Scientists came to the conclusion that the entropy of a rotating charged black hole in AdS can really be expressed by the number of microstates in space with fewer dimensions.