Why the Spacetime Embedding Incompressible Cores of Pulsars Must Be Conformally Flat?

Abstract

The multi-messenger observations of the merger event in GW170817 did not rule out the possibility that the remnant might be a dynamically stable neutron star with $\mathcal{M}_{rm}\geq 2.69 \,\mathcal{M}_{\odot}.$ Based on this and other recent events, I argue that the universal maximum density hypothesis should be revived. Accordingly, the central densities in the cores of ultra-compact objects must be upper-limited by the critical density number $n_{cr},$ beyond which supradense nuclear matter becomes purely incompressible. Based on the spacetime-matter coupling in GR, it is shown that the topology of spacetime embedding incompressible quantum fluids with $n =n_{cr}$ must be Minkowski flat, which implies that spacetime at the background of ultra-compact objects should be of bimetric type.