Speaker
Description
The Tolman~VII solution for a static perfect fluid sphere
to the Einstein equations is reexamined, and a closed form
class of equations of state (EOSs) is deduced for the first time.
These EOSs allow further analysis to be carried out, leading to a
viable model for compact stars with arbitrary boundary mass density
to be obtained. Explicit application
of causality conditions places further constraints on the model, and
recent observations of masses and radii of neutron stars prove to be
within the predictions of the model. The adiabatic index predicted
is $\gamma \geq 2,$ but self-bound crust solutions are not excluded
if we allow for higher polytropic indices in the crustal regions of
the star. The solution is also shown to obey known stability
criteria often used in modeling such stars. It is argued that
this solution provides realistic limits on models of compact stars,
maybe even independently of the type of EOS, since most of the EOSs
usually considered do show a quadratic density falloff to first
order, and this solution is the unique exact solution that has this
property.
