  In many circumstances the perfect fluid conservation equations can be
directly integrated to give a Geometric-Thermodynamic equation: typically that
the lapse $N$ is the reciprocal of the enthalphy $h$, ($ N=1/h$). This result
is aesthetically appealing as it depends only on the fluid conservation
equations and does not depend on specific field equations such as Einstein's.
Here the form of the Geometric-Thermodynamic equation is derived subject to
spherical symmetry and also for the shift-free ADM formalism. There at least
three applications of the Geometric-Thermodynamic equation, the most important
being to the notion of asympotic flatness and hence to spacetime exterior to a
star. For asymptotic flatness one wants $h\to 0$ and $N\to 1$ simultaneously,
but this is incompatible with the Geometric-Thermodynamic equation.
Observational data and asymptotic flatness are discussed. It is argued that a
version of Mach's principle does not allow asymptotic flatness.
