3.2 A Radical Change in Black Hole Structure

summary

As per Mathur, string theory must solve the information paradox to be a complete theory of quantum gravity.

The problem is that all the matter and energy (and therefore information) goes to the singularity at the center and cannot be recovered. Mathur claims that to solve the information paradox, black holes need a surface that can contain information.
In ordinary particle physics, particles are conceived as points. String theory says that elementary particles are “extended objects” (like strings or sheets) that have size.
If you put energy into a point particle it can only take the form of increased kinetic energy. If you put energy into an extended object like a string, there are two choices: it can go faster, or it can stretch.
Now, instead of particles all collapsing into a point, black hole formation could involve constituent strings undergoing extreme stretching and expansion. If the strings expand enough, they will never fall below the critical radius, thereby avoiding the creation of an event horizon or singularity altogether.
Calculations in string theory have found that the strings forming a black hole expand to approximately the size of the critical radius. Mathur takes this to be evidence that all black holes are actually fuzzballs.

The extra dimensions of string theory allow for new ideas of black hole structure.

The 10 dimensions described in string theory allow for an entirely new view of black holes – that they don’t have event horizons or spacetime interiors.
Instead, the spacetime manifold smoothly closes in on itself so that as you approach a black hole, you will actually loop around the surface instead of crossing it.
This leads to the interesting result that you cannot fall into a black hole. It is not an object within spacetime; it literally has no “inside”.
The mass of the matter forming the black hole manifests as the spacetime curvature of the surface.

These pseudo-black holes are called “fuzzballs”.

String theory offers a framework to eliminate the event horizon and infinitely dense singularity, the two most troubling aspects of classical black holes for the information paradox.
The curvature of the fuzzball surface is highly variable, creating an ultra-fine information-containing structure that gives this new, pseudo-black hole its name – “fuzzball”.
The information that was lost inside the classical black hole is now preserved in the twists and curves of spacetime on the fuzzball’s surface.

The fuzzball theory met resistance by those in favor of an alternative solution to the paradox – the postulate of small corrections.

Because the emitted Hawking particles come out of vacuum fluctuations, there is no information encoded in them that is specific to their source black hole.
The postulate of small corrections says that there could be small differences in vacuum states around different black holes. These differences in the vacuum would impart the emitted particles with some information about their source back hole.
As more and more particles are produced the information is slowly transmitted out of the black hole.
However, it does not matter how many subleading corrections are made to each pair production event; the problem is simply not solvable. Small perturbative corrections can only account for a tiny fraction of the total information.