-Apoorva Singh

From their existence to their thermodynamic properties, black holes have had some of the most intriguing paradoxes latched to their name. We may have some answers, but much is yet to be unveiled. One such paradox, THE BLACK HOLE INFORMATION PARADOX, although as unsolved as ever, might have found its way around some explanations. Most, if not all, of us, have heard about the two most important theoretical frameworks of physics that work on different domains: general relativity and quantum theory. While general relativity explains gravity as a result of a warped space-time to explain the interactions at a large scale, quantum theory uses the three non-gravitational forces to understand the Standard Model of particles. Both the theories, together, explain almost all the underlying phenomena in physics.

The theory of general relativity understands black holes as a very compact and dense region where gravity is strong enough to warp space-time, so much so that even light can't escape through their event horizon. In the 1970s, Hawking and his colleagues attempted a "semi-classical" approach to understanding the true nature of black holes. He showed that black holes emit radiation over time and, eventually, evaporate.

Nevertheless, the most significant shift was the fact that those radiations were utterly unstructured, leading us to realise that the final state of the radiation will only depend upon the mass, charge, and angular momentum. This would mean that the information about the initial state of the black hole was lost forever, which violates the principles of quantum physics.

So where does the information go?

In the 1990s, Susskind and ‘t Hooft suggested an idea on where the information may go, something we know as the "Holographic principle." This principle argues that when the matter crosses the event horizon, it leaves behind its imprint on a 2-Dimensional surface of the black holes. Later, the radiation carries it away, thus, preserving the information like a hologram. What is more surprising is that the 3-dimensional space of the black hole, with gravity, was somehow related to the 2-dimensional surface of the black hole, without gravity. However crazy as it may sound, this was an entirely different approach and hopefully might just be what we need.

In 1997, Juan Maldacena conjectured a mathematical bridge between string theory(with gravity) and quantum theory with fewer dimensions (without gravity), notoriously known as "ADS/CFT CORRESPONDENCE”.

Einstein's general theory of relativity represents gravity as a distortion of space-time. Based on how space-time is "curved," we define the models of the space-time continuum. There are three predictions about how a space-time continuum would appear: de-sitter space, Minkowski space, and anti-de-sitter space. De-sitter space results in a positively curved space-time without mass and energy present in it. Minkowski constitutes a flat space-time where the geodesics (the curve that joins the shortest distance between two points in space) are straight lines. The AdS space-time represents a rather interesting case where the curvature becomes negative, and the time-like geodesics intersect in far time, much like a hyperbolic diagram.

CFT OR CONFORMAL FIELD THEORY, in simple terms, means a scale-invariant quantum field theory. Consider zooming in on a picture on the phone and how the length scale changes. Conformal transformations are when the physics does not change with the scale length and looks the same (irrespective of the dimension). We could solve using mathematics in fewer dimensions rather than solving them in higher dimensions. Under these transformations, the angles are always preserved on any length scale.

Maldacena found evidence that claimed that string theory in a 5-dimensional AdS spacetime is equivalent to a strongly coupled conformal theory in 4-dimensions. This equivalence is famously known as the "ADS/CFT" or "Gauge /gravity duality." It is known to us that black holes have entropy. However, Bekenstein-Hawking entropy points to a bizarre fact that their entropy is proportional to the area of their event horizon instead of their volume. Now if black holes are to be described by the boundary in 4-dimensions, they have to exist in a bulk of 5-dimensions (much like a hologram).



This evidence fascinated the physicists to expand its application to the framework of our universe. While this conjecture was strong enough to transcend physicists to question more about its results than its existence, its relevance to our universe remains a question.

Because, not to our surprise, our universe is neither an AdSspace-time nor a scale-invariant space. When applied to our universe, this idea comes with many questions and ambiguities. Regardless, the idea of AdS/CFT correspondence was a significant breakthrough. There are applications of this conjecture outside the theories, too. One of the most exciting applications of this would be the "Quark-gluon plasma." QGP involves studying and recreating the high energy density conditions to understand how the matter was formed out of elementary particles- quarks and gluons after the Big Bang. AdS/CFT, undoubtedly, has become a magnificent tool for string theory, giving it a mathematically proven foundation .