  Dense nuclear matter is expected to be anisotropic due to effects such as
solidification, superfluidity, strong magnetic fields, hyperons,
pion-condesation. Therefore an anisotropic neutron star core seems more
realistic than an ideally isotropic one. We model anisotropic neutron stars
working in the Krori-Barua (KB) ansatz without preassuming an equation of
state. We show that the physics of general KB solutions is encapsulated in the
compactness. Imposing physical and stability requirements yields a maximum
allowed compactness $2GM/Rc^2 < 0.71$ for a KB-spacetime. We further input
observational data from numerous pulsars and calculate the boundary density. We
focus especially on data from the LIGO/Virgo collaboration as well as recent
independent measurements of mass and radius of miilisecond pulsars with white
dwarf companions by the Neutron Star Interior Composition Explorer (NICER). For
these data the KB-spacetime gives the same boundary density which surprisingly
equals the nuclear saturation density within the data precision. Since this
value designates the boundary of a neutron core, the KB-spacetime applies
naturally to neutron stars. For this boundary condition we calculate a maximum
mass of 4.1 solar masses.
