We examine the question of whether or not special relativity requires that the pressure must be less than the energy density of matter. To do this, we study a model of matter consisting of a classical one-dimensional lattice of point particles interacting via a potential satisfying the three-dimensional Klein-Gordon equation. Despite the fact that for this model the pressure p can exceed the energy density c2, giving rise to an adiabatic sound speed cs=(dpd)12>c, and in the low-frequency limit to a group velocity ddk>c and phase velocity k>c, for this type of lattice model, the formally calculated speed cs is not a signal speed and we find that the true signal propagation speed vsignal<c. Thus special relativity alone does not guarantee that p<c2. We briefly discuss other constraints on p, none of which seem sufficiently rigorous to rule out the possibility that p> at high densities. The significance of the present result for the upper mass limit of neutron stars and the existence of black holes is also considered.
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)