One person in particular suggested the following:
The first part of this is correct as described in the following formula for the speed of sound:
- E is a coefficient of stiffness, the bulk modulus (or the modulus of bulk elasticity for gases),
- is the density
Faster than light or near instant?
Six solar masses is only an upper bound on the size of a neutron star. More practical calculations estimate the upper limit as three solar masses. No objects confirmed as neutron stars are known that are larger than two solar masses; the mass is typically about 1.35 solar masses.
At the speed of light, or below?
In the link above, the following possibilities are explored by some people:
The distance the electromagnetic forces communicate movement through is not the space between the atoms (atoms are mostly empty space); it's the space between the electromagnetic fields of the electrons that interact with each other. That space is VERY CLOSE to a light year long in our experiment. The whole process of movement includes this space plus the distance particles (which can't be completely rigid) must travel to influence one another. In theory, as long as the formula used to calculate it does not provide undefined answers, none of the parameters stray off the current model of the universe we understand and the answer reaches c but isn't equal to it, there would be little reason to dismiss claims of the possibility that some materials may be able to transmit at almost such speeds. The best example I could find was in this following paper that concludes that evaluating equations at different densities for neutron stars all yield values for the speed of sound inferior to c.
Wait a minute! What about black holes?
Most of the theory before this deals with matter before it collapses into black holes. Most mathematical models explaining spacetime and force break down when they deal with black holes since they consist of matter that has collapsed further than a neutron star would have and has become so compressed it ceases to have actual volume. Despite my research I could not find much on the topic and the little I did points to the idea that a non-rotating black hole is completely stiff (has no adiabatic compressibility rate) while a rotating one has properties closer to neutron stars (see more: Compressibility of a Black Hole). While this tells us the possible properties of the matter in a black hole we have little idea (as far as I know) of how waves of sound would behave as they enter its event horizon or travel along its surface. A couple threads on StraightDope briefly touch this but it seems that sound doesn't travel at all because an infinitely compressible medium does not allow it to (as touched before when E becomes infinite in the speed of sound equation) or also because there is no space to travel the idea does not make sense.
Also, how would a plank-black hole structure be like?
Why is the elastic modulus relatively insensitive to changes in chemistry/heat treatment(...)
The Nature of Sound - The Physics Hyperbook
The Superluminal Scissors (similar Gedankenexperiment)