Let us limit ourselves to the static case . Fixing
,
, and then integrating
over
from zero to
, we find that the proper length of the equator of the star, i.e., its
circumference, as measured by a local observer, is equal to
. This is why
is called the
circumferential radius. Notice that Equation (90
) implies that the infinitesimal proper radial
distance (corresponding to the infinitesimal difference of radial coordinates
) is given by
.
From Einstein’s equations, we get the (relativistic) equations of hydrostatic equilibrium for a static spherically-symmetric star
Equation (92 Let us consider the differential Equations (92) and (93
), which determine the global structure of a
neutron star. They are integrated from the star center,
, with the boundary conditions
[
] and
. It is clear from Equation (92
), that pressure
is strictly decreasing with increasing
. The integration is continued until
, which
corresponds to the surface of the star, with radial coordinate
, usually called the star
radius.
The gravitational mass of the star is defined by . The mass
is the source of the
gravitational field outside the star (
), and creates an outer spacetime described by the
Schwarzschild metric,
The crust corresponds to the layer , where
determines the crust-core interface. The
depth below the stellar surface,
, is defined as the proper radial distance between the star surface and a
given surface of radius
. It is given by
An accreted crust has a different composition and thus a different EoS (stiffer) than the
ground-state crust (see Sections 4 and 5). For the comparison to be meaningful, however, these two
EoSs have to be calculated from the same nuclear Hamiltonian. We satisfied this by using in
both cases the same compressible liquid drop model of Mackie & Baym [277]. The plots of
for the ground state and accreted crust of a
neutron star are shown in
Figure 39
.
http://www.livingreviews.org/lrr-2008-10 | ![]() This work is licensed under a Creative Commons License. Problems/comments to |