The Black Hole Information Paradox

After WWII, there was a renewed interest among physicists in Einstein’s Theory of General Relativity (GR), and in particular, the concept of Black Holes (BHs). In fact, it was the American theoretical physicist John Archibald Wheeler, one of the people most frequently credited for this renewed interest, who popularised the term “Black Hole,” and was later lauded by Stephen Hawking as “the hero of the black hole story.”

According to GR, a BH is a region in spacetime where the gravity is so great, that nothing is said to escape, not even light. Once past what is known as the event horizon, a hypothetical boundary characteristic of that BH, there is simply no escaping the gravitational pull of the BH. Given this fact, it was logical to assume at that time in the 20th century, when GR was really beginning to gain traction in the physics world, that a BH couldn’t possibly emit
anything from its region, regardless of the nature of what was being emitted.

It wasn’t until the 1970s however, that physicists began to realise that perhaps GR alone wasn’t enough to fully describe the behaviour of these BHs. When Stephen Hawking, whose name is practically synonymous with BHs today, applied the theory of quantum mechanics to the theory of GR that described the behaviour of BHs, he discovered something rather interesting – that BHs in fact did emit something! Specifically, they emit a radiation that not only is capable of escaping the BH, but is also responsible for the loss of mass and rotational energy of the BH, which essentially causes the BH to “evaporate.” Today, this radiation is known as Hawking Radiation.

While Hawking was celebrated for this revelation within GR, there quickly arose a problem when the theory of his namesake radiation was taken to the max. Consider the following scenario: a BH evaporates via Hawking Radiation. In its final state, the radiation being emitted, according to Hawking, would be retaining information about only three specific parameters of the BH’s initial state – its total mass, its electric charge, and its angular momentum. (This notion is known as the No-hair Theorem). However, the number of physical states that have the same values of these very parameters is simply innumerable, and thus could all arrive at the same final state. From here, information about the BH’s initial state is said to be lost entirely!

And it is here that a mystery known as the Black Hole Information Paradox (BHIP) arises – both classical and quantum mechanics tell us that a system’s state at any given time should be able to give its value at any other given time, irrespective of past or future. So, if  Hawking’s theory is a direct violation of this very principle, then what exactly is going on?

In fact, the BHIP has had physicists scratching their heads for quite some time and has sparked many lively debates since first being encountered. One particular instance in 1997 saw Hawking, along the American theoretical physicist John Preskill, have a bet with American theoretical physicist, and good friend to both men, Kip Thorne, over whether the information emitted from a BH was truly lost. The occurrence is described in a popular science book by another fellow theoretical physicist Leonard Susskind, entitled The Black Hole War.

In conclusion, how does the BHIP resolve? Were Hawking’s initial calculations wrong? Did he just crack classical and quantum mechanics open like eggs? Or is there another physical discipline entirely that could provide the missing piece to the mystery behind BHs? Ultimately, there has been no real endpoint reached as of yet, but it has found itself under much discussion, for instance within the topics of both String Theory and Loop Quantum Gravity. Additionally, in the last years of his life, Hawking worked very closely with physicists Malcolm Perry and Andrew Strominger to try and determine the existence of “soft-hair” (additional parameters describing BHs) – this was ultimately Hawking’s final attempt not only to solve the BHIP, but also to uncover the unseen mysteries of BHs which his successors now have the great fortune of taking on.


(Published on behalf of Ben)