### 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) |
---|---|

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 |

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### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

*Physical Review D*,

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

**Must ultrabaric matter be superluminal?** / Caporaso, George J; Brecher, K.

Research output: Contribution to journal › Article

*Physical Review D*, vol. 20, no. 8, pp. 1823-1831. https://doi.org/10.1103/PhysRevD.20.1823

}

TY - JOUR

T1 - Must ultrabaric matter be superluminal?

AU - Caporaso, George J

AU - Brecher, K.

PY - 1979

Y1 - 1979

N2 - 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 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.

AB - 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 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.

UR - http://www.scopus.com/inward/record.url?scp=0000518354&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000518354&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.20.1823

DO - 10.1103/PhysRevD.20.1823

M3 - Article

AN - SCOPUS:0000518354

VL - 20

SP - 1823

EP - 1831

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 0556-2821

IS - 8

ER -