Acoustics of tachyon Fermi gas

TL;DR

This paper investigates the physical properties and stability conditions of a tachyon Fermi gas, analyzing causality, pressure, energy density, and shock wave phenomena within this hypothetical medium.

Contribution

It provides a detailed analysis of the stability, causality, and shock wave behavior of a tachyon Fermi gas, a novel theoretical exploration in tachyonic matter physics.

Findings

No stable tachyon matter below critical density and Fermi momentum.

Pressure and energy density cannot be arbitrarily small.

Shock waves do not survive at certain densities.

Abstract

We consider a Fermi gas of free tachyons as a continuous medium and find whether it satisfies the causality condition. There is no stable tachyon matter with the particle density below critical value $n_T$ and the Fermi momentum $k_F<\sqrt{\frac 32}m$ that depends on the tachyon mass $m$. The pressure $P$ and energy density $E$ cannot be arbitrary small, but the situation $P>E$ is not forbidden. Existence of shock waves in tachyon gas is also discussed. At low density $n_T<n<3.45n_T$ the tachyon matter remains stable but no shock wave do survive.