Noncommutative geometry is one of the approaches to investigate quantum gravity. We know that it is just an effective theory and would not be so promising to obtain the complete form of quantum gravity. However, it is true that we do not know what quantum geometries are and do not have a reliable way to write down such geometries without using manifolds. In that sense, the geometries inspired noncommutative geometry are interesting as a trial. In short, imaging such a space that we usually cannot detect or feel is extremely difficult. Noncommutative space/spacetime or spaces of discrete points/fuzzy objects do not accept our intuitive understanding.
Because of this circumstances, constructing the right intuition (or getting accustomed to, we may have to say) to the spacetimes we cannot touch easily is crucial. That is why I have been playing with fuzzy objects inspired from noncommutative geometry (of course, I know how much important to cultivate or try a top-down approach to quantum gravity and actually I have been doing a few things although I do not tell about them here.)
On the other hand, as a bottom-up approach, I am recently interested in the black hole solutions with Gaussian sources. These sources are inspired from the smearing by a noncommutative effect. Interestingly, these black hole solutions do exist, and their features are slightly different from ``normal" black holes in General Relativity. Many authors have already applied these black holes to various situations. They are not brand-new in some sense, but I am interested in them because they would be able to extend to a situation we treated in the current of the tachyon condensation and the deformation of D-branes by gravitational effects. Today I successfully constructed an extension of those black holes. I am going to check my calculation and write a paper about it as soon as possible before I start to feel it trivial.
Kobayashi Shinpei / 小林晋平 Website
Quantum Gravity Black Holes The Early Universe Metamaterials Mathematical Physics & Shapes