https://www.nature.com/articles/s41567-020-0914-9
Evidence for quark-matter cores in massive neutron stars by Eemeli Annala, Aleksi Vuorinen et al. in Nature Physics June 1, 2020 studies the mass distribution of a neutron star, assuming an arbitrary function f:
pressure = f (energy density of matter).
The authors mention that most hadronic models predict that the speed of sound squared, c_s^2, is equal to 0.5 or larger for high densities (we use natural units where c = 1).
Is it possible for the speed of sound to exceed the vacuum speed of light?
The answer is definitely yes, if we define the speed of sound as the phase speed of a well-formed periodic pressure wave (a "sine" wave). That is, as the speed of the crest of wave. A crest of an infinite sine wave does not transmit any information from a point A to a point B. The speed of the crest is not constrained by the universal signal speed limit, that is, the vacuum speed of light c.
https://motls.blogspot.com/2020/10/a-fun-calculation-of-maximum-speed-of.html
https://arxiv.org/abs/gr-qc/0703121
Lubos Motl in his blog post (2020), as well as George Ellis et al. in their arxiv paper (2007) claim that the "causal limit" for the speed of sound is the speed of light, c. But they fail to define what they exactly mean by the speed of sound.
When considering the stiffness properties of matter, the natural definition for the speed of sound is the phase speed, not the signal speed. The phase speed depends on the stiffness, and can exceed the speed of light.
string
wall |--------------------------| wall
As a practical example, consider a tense string which is attached to walls at its endpoints. If we pluck the string, we can create a standing wave into it. There is no speed limit for the phase speeds of the two sine wave components of the standing wave. The standing wave does not transport any information and is not constrained by the speed of light.
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