A study of the spherically symmetric eigenstates of the Klein-Gordon Einstein equations (Klein-Gordon geons) reveals that these geons have properties that are uniquely different from other gravitating systems that have been studied. The equilibrium states of these geons seem analogous to other gravitating systems; but when the question of stability is considered from a thermodynamical viewpoint, it is shown that, in contrast with other systems, adiabatic perturbations are forbidden. The reason is that the equations of state for the thermodynamical variables are not algebraic equations, but instead are differential equations. Consequently, the usual concept of an equation of state breaks down when Klein-Gordon geons are considered. When the question of stability is reconsidered in terms of infinitesimal perturbations of the basic fields, it is then found that Klein-Gordon geons will not undergo spherically symmetric gravitational collapse. Thus, Klein-Gordon geons are counterexamples to the conjecture that gravitational collapse is inevitable.

• Received 4 March 1968

DOI:https://doi.org/10.1103/PhysRev.172.1331