Why the spacetime embedding incompressible supradense nuclear matter is conformally flat?

TL;DR

This paper proposes that ultra-compact objects with incompressible supradense nuclear matter have a spacetime embedding that is conformally flat, suggesting a bimetric spacetime structure based on gravitational and matter coupling.

Contribution

It introduces the idea that the spacetime embedding of incompressible nuclear matter in ultra-compact objects is conformally flat, linking maximum density limits to spacetime topology.

Findings

Spacetime embedding of incompressible nuclear matter is conformally flat.

Ultra-compact objects may have a bimetric spacetime structure.

Maximum density hypothesis supports a Minkowski flat topology.

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.