  The Jeans analysis is studied in the first post-Newtonian limit. In other
words, the relativistic effects on the local gravitational instability are
considered for systems where characteristic velocity of the system and
corresponding gravitational field are higher than what permitted in Newtonian
limit. The dispersion relation for propagation of small perturbations is found
in the post-Newtonian approximation using two different techniques. A new Jeans
mass is derived and compared to the standard Jeans mass. In this limit, the
relativistic effects make the new Jeans mass to be smaller than the Newtonian
Jeans mass. Furthermore, the fractional difference between these two masses
increases when temperature/pressure of the system increases. Interestingly, in
this limit pressure can help the gravitational instability instead of
preventing it. Finally the results are applied to high temperature
astrophysical systems and the possibility of local fragmentations in some
relativistic systems is investigated.
