Black holes and string theory

Artist's rendition of a black holeDebashish Chakraborty

Recent astrophysical measurements have revealed the existence of a supermassive black hole at the centre of our galaxy, the Milky Way. These measurements also show that black holes are ubiquitous in our Universe. Thus, black holes do not just represent exotic solutions to Einstein's theory of General Relativity: they really exist in Nature.

A black hole possesses a surface, called the event horizon, which separates the interior of the black hole from the outside region. The area of this surface determines the thermodynamic Bekenstein-Hawking entropy of the black hole. This entropy should, according to Boltzmann, have a statistical interpretation in terms of microstates of the system, i.e. of the black hole. Thus, any candidate theory for a consistent theory of quantum gravity has to be able to identify these microstates, and their subsequent counting has to reproduce the thermodynamic entropy of the black hole.

String theory is a leading contender for a consistent theory of quantum gravity. With the pioneering work of Strominger and Vafa, it has become evident that it is possible to identify and to count black hole microstates in the context of string theory. At the current juncture, the black holes that are best understood are those that arise as solutions to theories of gravity with a certain amount of supersymmetry. Supersymmetry is a symmetry that relates bosons and fermions, and the amount of supersymmetry is calculated by the number of generators of this symmetry. These generators are called supercharges, and the black holes arising in string theory that are best understood are those with eight supercharges. Black holes of this type are supported by scalar fields, and this exhibit an interesting flow mechanism termed the attractor mechanism. This mechanism states that as one moves towards the event horizon of the black hole, the scalar fields flow to specific values at the event horizon, thereby losing all memory of their initial values far away from the horizon.

The attractor mechanism is at the heart of the recent progress in string theory in reproducing the thermodynamic black hole entropy by microstate counting. The latter exhibits fascinating connections with topological string theory and with the theory of automorphic forms. Topological string theory is a simplified topological version of full-fledged string theory that appears to capture the microstates of super symmetric black holes. Automorphic forms are an extension to several complex variables of the concept of analytic functions on the upper half-plane satisfying a certain functional equation.

In addition, the microstates should also be captured by the enigmatic AdS2/CFT1 correspondence. The AdS/CFT correspondence, discovered by Maldacena, describes a deep connection between gravitational theories in d-dimensional spacetimes and field theories in one dimension lower. It states that quantum gravity (closed string theory) in anti-de Sitter spacetimes has an equivalent (dual) description in terms of conformal field theories (open string theory) in one dimension lower, living at the boundary of anti-de Sitter spacetime. The AdS2/CFT1 correspondence is a poorly understood example of this duality.

Despite much work in this area, our understanding of black holes with eight supercharges is far from being complete, and it is likely that many more surprises will emerge. Ultimately the goal is to obtain an understanding of realistic black holes, i.e. of black holes with no super symmetry at all.

The writer is a student at the Dept. of Computer Science and Engineering, BRAC University