  We determine the caloric curves of classical self-gravitating systems at
statistical equilibrium in general relativity. In the classical limit, the
caloric curves of a self-gravitating gas depend on a unique parameter
$\nu=GNm/Rc^2$, called the compactness parameter, where $N$ is the particle
number and $R$ the system's size. Typically, the caloric curves have the form
of a double spiral. The "cold spiral", corresponding to weakly relativistic
configurations, is a generalization of the caloric curve of nonrelativistic
classical self-gravitating systems. The "hot spiral'", corresponding to
strongly relativistic configurations, is similar (but not identical) to the
caloric curve of the ultrarelativistic self-gravitating black-body radiation.
We introduce two types of normalization of energy and temperature in order to
obtain asymptotic caloric curves describing respectively the cold and the hot
spirals in the limit $\nu\rightarrow 0$. As the number of particles increases,
the cold and the hot spirals approach each other, merge at $\nu'_S=0.128$, form
a loop above $\nu_S=0.1415$, reduce to a point at $\nu_{\rm max}=0.1764$, and
finally disappear. Therefore, the double spiral shrinks when the compactness
parameter $\nu$ increases, implying that general relativistic effects render
the system more unstable. We discuss the nature of the gravitational collapse
at low and high energies with respect to a dynamical (fast) or a
thermodynamical (slow) instability.
