Black holes are one of the most famous predictions of Einstein’s theory of general relativity. They are trapped regions of space, characterised by electric charge, mass and rate of rotation, from which nothing can escape. Supermassive black holes exist at the centre of probably every galaxy, with a mass ten to one hundred billion times greater than the sun.
General relativity provides us with a broad description of black hole dynamics. But any successful quantum theory of gravity should be able to explain their microscropic origins.
The quantity called entropy gives the number of microscopic configurations that could produce a given measurable observation. Stephen Hawking famously discovered black holes have both a temperature and an entropy. Moreover the entropy is precisely one quarter the area of the event horizon (black hole boundary) in appropriate units. Physicists want to understand the origin of this entropy. How is it configured on a microscopic scale?
For certain supersymmetric black holes – mathematical cousins of those that exist in the real world – string theory has been able to answer this precisely. In these cases the microscopic configurations can be counted using D-branes, fully agreeing with Hawking’s result. The calculation was first done by Strominger and Vafa in 1996 for a class of 5-dimensional black holes.
This method has since been extended to black holes in many different dimensions. More precise entropy computations are continually undertaken. There is an ongoing program that applies these techniques to further examples.
A second well-known problem concerns whether information is lost in black holes. An ordered physical state, like an encyclopedia, contains information. Throw the encyclopedia into a black hole, and the information seems to disappear behind the event horizon to be lost forever.
Over the last forty years physicists have learnt that black holes evaporate. According to Hawking’s partially quantum calculations, an evaporating black hole will emit only heat energy: there will be no traces of the objects that formed the black hole. But this seems to contradict quantum mechanics, which claims that information is never lost. Which is right?
String theorists attack the problem using the AdS/CFT correspondence. This relates purely gravitational systems with purely quantum counterparts. On the gravity side, a black hole can form, grow and evaporate. This process becomes an evolving quantum state on the QFT side. Quantum mechanics then holds, and information is not lost.
This is an example of a holographic argument. These play a vital role in research today and may become cornerstones of future physics. The method is generally viewed as answering the question of whether information is lost. However it is not very constructive: it doesn’t tell us what actually happens when black holes evaporate.