Massive Neutron Stars and White Dwarfs as Noncommutative Fuzzy Spheres

Over the last couple of decades, there are direct and indirect evidences for massive compact objects than their conventional counterparts. A couple of such examples are super-Chandrasekhar white dwarfs and massive neutron stars. The observations of more than a dozen peculiar over-luminous type Ia supernovae predict their origins from super-Chandrasekhar white dwarf progenitors. On the other hand, recent gravitational wave detection and some pulsar observations argue for massive neutron stars, lying in the famous mass-gap between lowest astrophysical black hole and conventional highest neutron star masses. We show that the idea of a squashed fuzzy sphere, which brings in noncommutative geometry, can self-consistently explain either of the massive objects as if they are actually fuzzy or squashed fuzzy spheres. Noncommutative geometry is a branch of quantum gravity. If the above proposal is correct, it will provide observational evidences for noncommutativity.