### 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)

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## Cite this

*Physical Review D*,

*20*(8), 1823-1831. https://doi.org/10.1103/PhysRevD.20.1823