Abstract
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.
Original language | English (US) |
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Pages (from-to) | 1823-1831 |
Number of pages | 9 |
Journal | Physical review D |
Volume | 20 |
Issue number | 8 |
DOIs | |
State | Published - 1979 |
Externally published | Yes |
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)