## Proposed solutions

Here we discuss the various solutions that have been proposed to deal with the problems created by the large number of light objects.

We have seen that the attractive nature of gravity leads to a curious situation. We can start with a heavy mass $$M$$, which has an energy $$E=Mc^2$$. We can then cancel this energy by placing small masses $$m$$ close by, so that we make use of the negative potential energy of gravity. In this way we can bring the energy of the resulting configuration - the 'object' to a very small value. Using Einstein's relation again, we find that this small energy corresponds to a small mass for the object.

A priori, it appears that we could bring this mass all the way down to zero. But once the mass gets down to the planck scale - $$10^{-5}$$ grams, there could be new effects of quantum gravity that we do not at present understand. So it is not clear if the mass can indeed be brought down all the way to zero. But it is enough for our purposes that we assume that it can be brought down to around the planck mass.

We have then observed that the number of such planck mass objects will be infinite. This, as we will see, poses a serious problem for quantum theory. Let us now see the various types of solutions that people have found:

(a) Information loss : Let us suppose that the mass of such objects could indeed be brought down all the way to zero. Since we normally expect that only empty space has zero energy, we require that any zero energy object of the above kind vanish, leaving nothing behind.

This postulate certainly gets rid of the problem: we do not have to deal with any of these curious objects. But in this case we lose the information describing the object: the mass and nature of the heavy mass $$M$$, and also the detailed pattern of the masses $$m$$. Such a loss of information is incompatible with the basic structure of physics as we know it, and in particular with the tenets of quantum mechanics. This situation would be analogous to the solution proposed by Hawking's in 1974 in his original paper on the information paradox, where he advocated that we alter the basic structure of quantum theory. Not many people accept this proposal today.

(b) Remnants: We assume that the objects found above (with zero or small overall energy) do exist. Such objects are called remnants, for a reason we will see shortly. Some people working in the area of general relativity are comfortable with this option. But we we have noted above, it is not clear how we can get a good formulation of quantum theory if an infinite number of remnants exist.

(c) Fuzzballs: Some physical effect may prevent us from placing the mass $$m$$ inside the horizon radius $$r_0$$. In that case we cannot make the kind of small mass object that is at the root of the problem. In string theory, such an effect is found through the 'fuzzball construction'.

The figure on the right depicts a fuzzball: due to a quantum effect, it turns out that the entire structure lies is just outside the horizon surface rather than inside.

(d) "New" physics: We postulate that novel physical behavior arises when such zero mass objects form. For example we may require that different observers see the same reality differently (different 'pictures'). One observer may think that the structure of the object resides inside the horizon (picture 1), while another may see this same structure encoded in some bits that are far away from the object (picture 2).